Search results for: propagation equation

Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: R. Z. Wang, B. C. Lin, C. H. Huang

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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.

Keywords: VFIFE, crack propagation, fictitious crack model, crack critical

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: S. K. Jain, M. K. Mishra

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Oblique propagation of ion-acoustic solitons in magnetized electron-positron-ion (EPI) plasma with warm adiabatic ions and isothermal electrons has been studied. Korteweg-de Vries (KdV) equation using reductive perturbation method has been derived for the system, which admits an obliquely propagating soliton solution. It is found that for the selected set of parameter values, the system supports only compressive solitons. Investigations reveal that an increase in positron concentration diminishes the amplitude as well as the width of the soliton. It is also found that the temperature ratio of electron to positron (γ) affects the amplitude of the solitary wave. An external magnetic field do not affect the amplitude of ion-acoustic solitons, but obliqueness angle (θ), the angle between wave vector and magnetic field affects the amplitude. The amplitude of the ion-acoustic solitons increases with increase in angle of obliqueness. Magnetization and obliqueness drastically affect the width of the soliton. An increase in ionic temperature decreases the amplitude and width. For the fixed set of parameters, profiles have been drawn to study the combined effect with variation of two parameters on the characteristics of the ion-acoustic solitons (i.e., amplitude and width). The result may be applicable to plasma in the laboratory as well as in the magnetospheric region of the earth.

Keywords: ion-acoustic solitons, Korteweg-de Vries (KdV) equation, magnetized electron-positron-ion (EPI) plasma, reductive perturbation method

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Yanpei Zhen

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The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background.

Keywords: Darboux transformation, periodic wave, Rogue wave, separating the variables

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Victor Chomel, Maziyar Panahi, David Chavalarias

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Misinformation has taken an increasingly worrying place in social media. Propagation patterns are closely linked to the structure of communities. This study proposes a method of community analysis based on a combination of centrality indicators for the network and its main communities. The objective is to establish a link between the stability of the communities over time, the social ascension of its members internally, and the propagation of information in the community. To this end, data from the debates about global warming and political communities on Twitter have been collected, and several tens of millions of tweets and retweets have helped us better understand the structure of these communities. The quantification of this stability allows for the study of the propagation of information of any kind, including disinformation. Our results indicate that the most stable communities over time are the ones that enable the establishment of nodes capturing a large part of the information and broadcasting its opinions. Conversely, communities with a high turnover and social ascendancy only stabilize themselves strongly in the face of adversity and external events but seem to offer a greater diversity of opinions most of the time.

Keywords: community analysis, disinformation, misinformation, Twitter

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Authors: Balasundaram Prasaant, Ploix Stephane, Delinchant Benoit, Muresan Cristian

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Hardware in Loop (HIL) testing is done to test and validate a particular product especially in building technology. When it comes to building technology, it is more important to test the products for their efficiency. The test rig in the HIL simulator may contribute to some uncertainties on measured efficiency. The uncertainties include physical uncertainties and scenario-based uncertainties. In this paper, a simple uncertainty analysis framework for an HIL setup is shown considering only the physical uncertainties. The entire modeling of the HIL setup is done in Dymola. The uncertain sources are considered based on available knowledge of the components and also on expert knowledge. For the propagation of uncertainty, Monte Carlo Simulation is used since it is the most reliable and easy to use. In this article it is shown how an HIL setup can be modeled and how uncertainty propagation can be performed on it. Such an approach is not common in building energy analysis.

Keywords: energy in buildings, hardware in loop testing, modelica modelling, Monte Carlo simulation, uncertainty propagation

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Reza Hedayati, Meysam Jahanbakhshi

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In this work, Fracture Mechanics is used to predict crack propagation in the adhesive joining aluminum and composite plates. Three types of loadings and two types of glass-epoxy composite sequences: [0/90]2s and [0/45/-45/90]s are considered for the composite plate. Therefore, 2*3=6 cases are considered and their results are compared. The debonding initiation load, complete debonding load, crack face profile and load-displacement diagram have been compared for the six cases.

Keywords: adhesive joint, debonding, fracture, LEFM, APDL

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Authors: Bin Mu, Site Li, Shijin Yuan

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Under the circumstance of environment deterioration, people are increasingly concerned about the quality of the environment, especially air quality. As a result, it is of great value to give accurate and timely forecast of AQI (air quality index). In order to simplify influencing factors of air quality in a city, and forecast the city’s AQI tomorrow, this study used MATLAB software and adopted the method of constructing a mathematic model of PCA-GABP to provide a solution. To be specific, this study firstly made principal component analysis (PCA) of influencing factors of AQI tomorrow including aspects of weather, industry waste gas and IAQI data today. Then, we used the back propagation neural network model (BP), which is optimized by genetic algorithm (GA), to give forecast of AQI tomorrow. In order to verify validity and accuracy of PCA-GABP model’s forecast capability. The study uses two statistical indices to evaluate AQI forecast results (normalized mean square error and fractional bias). Eventually, this study reduces mean square error by optimizing individual gene structure in genetic algorithm and adjusting the parameters of back propagation model. To conclude, the performance of the model to forecast AQI is comparatively convincing and the model is expected to take positive effect in AQI forecast in the future.

Keywords: AQI forecast, principal component analysis, genetic algorithm, back propagation neural network model

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Authors: Gül Çevik

Abstract:

This paper summarizes the work conducted to assess the root cause of the failure of a medium commercial vehicle leaf spring failed in service. Macro- and micro-fractographic analyses by scanning electron microscope as well as material verification tests were conducted in order to understand the failure mechanisms and root cause of the failure. Findings from the fractographic analyses indicated that failure mechanism is fatigue. Crack initiation was identified to have occurred from a point on the top surface near to the front face and to the left side. Two other crack initiation points were also observed, however, these cracks did not propagate. The propagation mode of the fatigue crack revealed that the cyclic loads resulting in crack initiation and propagation were unidirectional bending. Fractographic analyses have also showed that the root cause of the fatigue crack initiation and propagation was loading the part above design stress. Material properties of the part were also verified by chemical composition analysis, microstructural analysis by optical microscopy and hardness tests.

Keywords: leaf spring, failure analysis, fatigue, fractography

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Authors: Ajoy Kumar Das, Prasenjit Dey

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Heat transfer due to forced convection of copper water based nanofluid has been predicted by Artificial Neural network (ANN). The present nanofluid is formed by mixing copper nano particles in water and the volume fractions are considered here are 0% to 15% and the Reynolds number are kept constant at 100. The back propagation algorithm is used to train the network. The present ANN is trained by the input and output data which has been obtained from the numerical simulation, performed in finite volume based Computational Fluid Dynamics (CFD) commercial software Ansys Fluent. The numerical simulation based results are compared with the back propagation based ANN results. It is found that the forced convection heat transfer of water based nanofluid can be predicted correctly by ANN. It is also observed that the back propagation ANN can predict the heat transfer characteristics of nanofluid very quickly compared to standard CFD method.

Keywords: forced convection, square cylinder, nanofluid, neural network

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Haowei Chen, Kaiqi Xiong

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This paper aims to answer how malware will propagate in Wireless Mesh Networks (WMNs) and how communication radius and distributed density of nodes affects the process of spreading. The above analysis is essential for devising network-wide strategies to counter malware. We answer these questions by developing an improved dynamical system that models malware propagation in the area where nodes were uniformly distributed. The proposed model captures both the spatial and temporal dynamics regarding the malware spreading process. Equilibrium and stability are also discussed based on the threshold of the system. If the threshold is less than one, the infected nodes disappear, and if the threshold is greater than one, the infected nodes asymptotically stabilize at the endemic equilibrium. Numerical simulations are investigated about communication radius and distributed density of nodes in WMNs, which allows us to draw various insights that can be used to guide security defense.

Keywords: Bluetooth security, malware propagation, wireless mesh networks, stability analysis

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Authors: Reza Hedayati, Meysam Jahanbakhshi

Abstract:

In this work, Fracture Mechanics is used to predict crack propagation in the adhesive jointing aluminum and composite plates. Three types of loadings and two types of glass-epoxy composite sequences: [0/90]2s and [0/45/-45/90]s are considered for the composite plate. Therefore 2*3=6 cases are considered and their results are compared. The debonding initiation load, complete debonding load, crack face profile and load-displacement diagram have been compared for the six cases.

Keywords: fracture, adhesive joint, debonding, APDL, LEFM

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Authors: Olukunle C. Olawole, Dilip Kumar De

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We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

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Authors: R. Loukil, M. Chtourou, T. Damak

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This paper investigates the training of multilayer neural network using the classic approach. Then, for estimation purposes, we suggest the use of a specific neural observer that we study its training algorithm which is the back-propagation one in the case of the disponibility of the state and in the case of an unmeasurable state. A MATLAB simulation example will be studied to highlight the usefulness of this kind of observer.

Keywords: training, estimation purposes, neural observer, back-propagation, unmeasurable state

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Authors: Seon Soon Choi

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The fatigue crack growth is stochastic because of the fatigue behavior having an uncertainty and a randomness. Therefore, it is necessary to determine the probability distribution of a grown crack size at a specific fatigue crack propagation life for maintenance of structure as well as reliability estimation. The essential purpose of this study is to present the good probability distribution fit for the grown crack size at a specified fatigue life in a rolled magnesium alloy under different specimen thickness conditions. Fatigue crack propagation experiments are carried out in laboratory air under three conditions of specimen thickness using AZ31 to investigate a stochastic crack growth behavior. The goodness-of-fit test for probability distribution of a grown crack size under different specimen thickness conditions is performed by Anderson-Darling test. The effect of a specimen thickness on variability of a grown crack size is also investigated.

Keywords: crack size, fatigue crack propagation, magnesium alloys, probability distribution, specimen thickness

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Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

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In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

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Authors: Feng Tao, Han Ye, Shaoyi Liao

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City constructions collapse after earthquake and people will be buried under ruins. Search and rescue should be conducted as soon as possible to save them. Therefore, according to the complicated environment, irregular aftershocks and rescue allow of no delay, a kind of target localization method based on RSSI (Received Signal Strength Indication) is proposed in this article. The target localization technology based on RSSI with the features of low cost and low complexity has been widely applied to nodes localization in WSN (Wireless Sensor Networks). Based on the theory of RSSI transmission and the environment impact to RSSI, this article conducts the experiments in five scenes, and multiple filtering algorithms are applied to original RSSI value in order to establish the signal propagation model with minimum test error respectively. Target location can be calculated from the distance, which can be estimated from signal propagation model, through improved centroid algorithm. Result shows that the localization technology based on RSSI is suitable for large-scale nodes localization. Among filtering algorithms, mixed filtering algorithm (average of average, median and Gaussian filtering) performs better than any other single filtering algorithm, and by using the signal propagation model, the minimum error of distance between known nodes and target node in the five scene is about 3.06m.

Keywords: signal propagation model, centroid algorithm, localization, mixed filtering, RSSI

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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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: Xuri Tang, Ting Pan

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Metaphor institutionalization refers to the propagation of a metaphor that leads to its acceptance in speech community as a norm of the language. Such knowledge is important to both theoretical studies of metaphor and practical disciplines such as lexicography and language generation. This paper reports an empirical study of metaphor institutionalization of 14 Chinese metaphors. It first explores the pattern of metaphor institutionalization by fitting the logistic function (or S-shaped curve) to time series data of conventionality of the metaphors that are automatically obtained from a large-scale diachronic Chinese corpus. Then it reports a questionnaire-based survey on the propagation scale of each metaphor, which is measured by the average number of subjects that can easily understand the metaphorical expressions. The study provides two pieces of evidence supporting the hypothesis that metaphor institutionalization is a phrase transition: (1) the pattern of metaphor institutionalization is an S-shaped curve and (2) institutionalized metaphors generally do not propagate to the whole community but remain in equilibrium state. This conclusion helps distinguish metaphor institutionalization from topicalization and other types of semantic change.

Keywords: metaphor institutionalization, phase transition, propagation scale, s-shaped curve

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Authors: Hamid Hamli Benzahar

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The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.

Keywords: composite beam, shear deformation, moments, finites elements

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Authors: Khaled Moaddy

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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

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