Search results for: exact solutions

Authors: M. Benhamida, Kh. Bouamama, P. Djemia

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We investigate by first-principles pseudo-potential calculations the composition dependence of lattice parameter, hardness and elastic properties of ternary disordered solid solutions Ti(1-x)Ta(x)N (1>=x>=0) with B1-rocksalt structure. Calculations use the coherent potential approximation with the exact muffin-tin orbitals (EMTO) and hardness formula for multicomponent covalent solid solution proposed. Bulk modulus B shows a nearly linear behaviour whereas not C44 and C’=(C11-C12)/2 that are not monotonous. Influences of vacancies on hardness of off-stoichiometric transition-metal nitrides TiN(1−x) and TaN(1−x) are also considered.

Keywords: transition metal nitride materials, elastic constants, hardness, EMTO

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Authors: K. N. S. Kasi Viswanadham

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Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Keywords: collocation method, coupled system, cubic b-splines, mesh points

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Authors: Rajendra Kumar Dubey

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Einstein’s field equations with variable cosmological term Λ are considered in the presence of viscous fluid for Bianchi type I space time. Exact solutions of Einstein’s field equations are obtained by assuming cosmological term Λ Proportional to (R is a scale factor and m is constant). We observed that the shear viscosity is found to be responsible for faster removal of initial anisotropy in the universe. The physical significance of the cosmological models has also been discussed.

Keywords: bianchi type, I cosmological model, viscous fluid, cosmological constant Λ

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Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: S. S. Bendib, L. W. Mouss, S. Kalla

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This paper proposes a self-organization-based approach for real-time systems design. The addressed issue is the mapping of an application onto an architecture of heterogeneous processors while optimizing both makespan and reliability. Since this problem is NP-hard, a heuristic algorithm is used to obtain efficiently approximate solutions. The proposed approach takes into consideration the quality as well as the diversity of solutions. Indeed, an alternate treatment of the two objectives allows to produce solutions of good quality while a self-organization approach based on the neighborhood structure is used to reorganize solutions and consequently to enhance their diversity. Produced solutions make different compromises between the makespan and the reliability giving the user the possibility to select the solution suited to his (her) needs.

Keywords: embedded real-time systems design, makespan, reliability, self-organization, compromises

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Authors: Po-Jen Su, Huann-Ming Chou

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In this article we uses the residual correction method to deal with transient thermoelastic problems with a hollow spherical region when the continuum medium possesses spherically isotropic thermoelastic properties. Based on linear thermoelastic theory, the equations of hyperbolic heat conduction and thermoelastic motion were combined to establish the thermoelastic dynamic model with consideration of the deformation acceleration effect and non-Fourier effect under the condition of transient thermal shock. The approximate solutions of temperature and displacement distributions are obtained using the residual correction method based on the maximum principle in combination with the finite difference method, making it easier and faster to obtain upper and lower approximations of exact solutions. The proposed method is found to be an effective numerical method with satisfactory accuracy. Moreover, the result shows that the effect of transient thermal shock induced by deformation acceleration is enhanced by non-Fourier heat conduction with increased peak stress. The influence on the stress increases with the thermal relaxation time.

Keywords: maximum principle, non-Fourier heat conduction, residual correction method, thermo-elastic response

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Mohammad Hossein Ahmadi, Vahid Haghighatdoost

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Spatial databases have been an active area of research over years. In this paper, we study how to answer the General Time-Dependent Sequenced Route queries. Given the origin and destination of a user over a time-dependent road network graph, an ordered list of categories of interests and a departure time interval, our goal is to find the minimum travel time path along with the best departure time that minimizes the total travel time from the source location to the given destination passing through a sequence of points of interests belonging to each of the specified categories of interest. The challenge of this problem is the added complexity to the optimal sequenced route queries, where we assume that first the road network is time dependent, and secondly the user defines a departure time interval instead of one single departure time instance. For processing general time-dependent sequenced route queries, we propose two solutions as Discrete-Time and Continuous-Time Sequenced Route approaches, finding approximate and exact solutions, respectively. Our proposed approaches traverse the road network based on A*-search paradigm equipped with an efficient heuristic function, for shrinking the search space. Extensive experiments are conducted to verify the efficiency of our proposed approaches.

Keywords: trip planning, time dependent, sequenced route query, road networks

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Authors: Seyed Habib A. Rahmati, Mohamad Hasan Sadeghpour, Parsa Fallah Sheikhlari

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Location quotient (LQ) is a comparison technique that represents emphasized economic structure of single zone versus the standard area to identify specialty for every zone. In another words, the exact calculation of this metric can show the main core competencies and critical capabilities of an area to the decision makers. This research focus on the exact calculation of the LQ for an Iranian Province called Qazvin and within a case study introduces LQ of the capable industries of Qazvin. Finally, through different graphs and tables, it creates an opportunity to compare the recognized capabilities.

Keywords: location quotient, case study, province analysis, core competency

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Authors: S. Henine, A. Youkana

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This work is devoted to study the global existence and asymptotic behavior of solutions for Gierer-Meinhardt systems arising in biological phenomena. We prove that the solutions are global and uniformly bounded by a positive constant independent of the time. Our technique is based on Lyapunov functional argument. Under suitable conditions, we established a result on the asymptotic behavior of solutions. These results are valid for any positive continuous initial data, and improve some recently results established.

Keywords: asymptotic behavior, Gierer-Meinhardt systems, global existence, Lyapunov functional

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Authors: Michael Danilov, Sergei Iskakov, Vladimir Mazurenko

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The present paper describes a high-performance parallel realization of an exact diagonalization solver for quantum-electron models in a shared memory computing system. The proposed algorithm contains a storage format for efficient computing eigenvalues and eigenvectors of a quantum electron Hamiltonian matrix. The results of the test calculations carried out for 15 sites Hubbard model demonstrate reduction in the required memory and good multiprocessor scalability, while maintaining performance of the same order as compressed row storage.

Keywords: sparse matrix, compressed format, Hubbard model, Anderson model

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: T. Boonraksa, B. Marungsri

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This paper presents the experimental results on role of ionic solutions affect water treeing propagation in cross-linked polyethylene insulation for high voltage cable. To study the water treeing expansion due to the ionic solutions, discs of 4mm thickness and 4cm diameter were taken from 115 kV XLPE insulation cable and were used as test specimen in this study. Ionic solutions composed of CuSO4, FeSO4, Na2SO4 and K2SO4 were used. Each specimen was immersed in 0.1 mole ionic solutions and was tested for 120 hrs. under a voltage stress at 7 kV AC rms, 1000 Hz. The results show that Na2SO4 and CuSO4solutions play an important role in the expansion of water treeing and cause degradation of the cross-linked polyethylene (XLPE) in the presence of the applied electric field.

Keywords: ionic solutions, water treeing, water treeing expansion, cross-linked polyethylene (XLPE)

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Authors: Shankar Kambhampaty, Harish Rohan Kambhampaty

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Data in IT systems in enterprises has been growing at a phenomenal pace. This has provided opportunities to run analytics to gather intelligence on key business parameters that enable them to provide better products and services to customers. While there are several artificial intelligence (AI/ML) and business intelligence (BI) tools and technologies available in the marketplace to run analytics, there is a need for an integrated view when developing intelligent solutions in enterprises. This paper progressively elaborates a reference model for enterprise solutions, builds an integrated view of data, information, and intelligence components, and presents a reference architecture for intelligent enterprise solutions. Finally, it applies the reference architecture to an insurance organization. The reference architecture is the outcome of experience and insights gathered from developing intelligent solutions for several organizations.

Keywords: architecture, model, intelligence, artificial intelligence, business intelligence, AI, BI, ML, analytics, enterprise

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Authors: Yang Zhou, Chen Hao, Ma Xiaoping

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This paper briefly mentions the micro controller unit, and then goes into details about the exact regulations for SRM. Firstly, it proposes the main driving state control for motor and the importance of the motor position sensor. For different speed, the controller will choice various styles such as voltage chopper control, angle position control and current chopper control for which owns its advantages and disadvantages. Combining the strengths of the three discrepant methods, the main control chip will intelligently select the best performing control depending on the load and speed demand. Then the exact flow diagram is showed in paper. At last, an experimental platform is established to verify the correctness of the proposed theory.

Keywords: switched reluctance motor, dspic microcontroller, current chopper

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Authors: Z. Aziz, S. Terkhi, Y. Sefir, R. Djelti, S. Bentata

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The effect of a uniform electric field across multibarrier systems (InAs/InxGa1-xAs) is exhaustively explored by a computational model using exact airy function formalism and the transfer-matrix technique. In the case of biased DFHBSL structure a strong reduction in transmission properties was observed and the width of the miniband structure linearly decreases with the increase of the applied bias. This is due to the confinement of the states in the miniband structure, which becomes increasingly important (Wannier-Stark Effect).

Keywords: dimer fibonacci height barrier superlattices, singular extended state, exact airy function, transfer matrix formalism

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Authors: Jiwon Lee, Si-hwan Jang, Sanghyun Joo

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The popularity of emoticons are on the rise since the mobile messengers are generalized. At the same time, few problems of emoticons are also occurred due to innate characteristics of emoticons. Too many emoticons make difficult people to select one which is well-suited for user's intention. On the contrary to this, sometimes user cannot find the emoticon which expresses user's exact intention. Poor information delivery of emoticon is another problem due to a major part of current emoticons are focused on emotion delivery. In this situation, we propose a new concept of emoticons, editable emoticons, to solve above drawbacks of emoticons. User can edit the components inside the proposed editable emoticon and send it to express his exact intention. By doing so, the number of editable emoticons can be maintained reasonable, and it can express user's exact intention. Further, editable emoticons can be used as information deliverer according to user's intention and editing skills. In this paper, we propose the concept of editable emoticons and schema based editable emoticon description method. The proposed description method is 200 times superior to the compared screen capturing method in the view of transmission bandwidth. Further, the description method is designed to have compatibility since it follows MPEG-UD international standard. The proposed editable emoticons can be exploited not only mobile applications, but also various fields such as education and medical field.

Keywords: description schema, editable emoticon, emoticon transmission, mobile applications

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Nhabhat Chaimongkol

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Human capital is one of the factors that are vital for economic growth. This is especially true as humans will face increasingly more forms of disruptive technology in the near future. Therefore, there is a need to develop human capital in order to overcome the current uncertainty in the global economy and the future of jobs. In recent years, Thailand has increasingly devoted more attention to developing its human capital. The Thai government has raised this issue in its national agenda, which is part of its 20-year national strategy. Currently, there are multiple challenges and solutions regarding this issue. This study aims to find out what are the challenges and solutions to human capital development in Thailand. The research in this study uses mixed methods consisting of quantitative and qualitative research methods. The results show that while Thailand has many plans to develop human capital, it is still lacking the necessary actions and integrations that are required to achieve its goals. Finally, the challenges and solutions will be discussed in detail.

Keywords: challenges, human capital, solutions, Thailand

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Authors: Doo Ki Lee, Man Young Kim

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The Urea-Selective Catalytic Reduction (SCR) system is considered to be the most promising technology to fulfill the stringent emission regulation. In the Urea-SCR system, the urea solutions are used as the reducing agent, which is a eutectic composition (32.5wt% of urea). The advantage of this eutectic compositions is that it has a low freezing point approximately at -11 ℃, however, the problem of freezing occurs at low-temperature levels below that freezing point. To prevent freezing of urea solutions, we need heating systems that can melt by heating the frozen urea solutions in urea storage tank at low-temperature environment. In this study, therefore, a numerical investigation of three-dimensional unsteady heating problems analyzed to find the melting characteristics of the urea solutions on melting process. In this work, it can be found that the urea melting initiated by heat conduction from the heater is enhanced by the natural convection inside the melted liquid urea solutions due to the temperature difference. Also, liquid urea solutions are initially concentrated on the upper parts of the urea sender module.

Keywords: urea solution, melting, heat conduction, natural convection, liquid fraction, phase change

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Triloki Nath, R. K. Gupta, L. P. Singh

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The aim of this paper is to find the new exact solution of the blast wave problem in one-dimensional unsteady adiabatic flow for generalized geometry in a compressible, inviscid ideal gas with dust particles. The density of the undisturbed region is assumed to vary according to a power law of the distance from the point of explosion. The exact solution of the problem in form of a power in the distance and the time is obtained. Further, the behaviour of the total energy carried out by the blast wave for planar, cylindrically symmetric and spherically symmetric flow corresponding to different Mach number of the fluid flow in dusty gas is presented. It is observed that the presence of dust particles in the gas yields more complex expression as compared to the ordinary Gasdynamics.

Keywords: shock wave, blast wave, dusty gas, strong shock

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Somayeh Nezami

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The management of financial and human resources of police in metropolitans requires many information and exact plans to reduce a rate of crime and increase the safety of the society. Geographical Information Systems have an important role in providing crime maps and their analysis. By using them and identification of crime hot spots along with spatial presentation of the results, it is possible to allocate optimum resources while presenting effective methods for decision making and preventive solutions. In this paper, we try to explain and compare between some of the methods of hot spots analysis such as Mode, Fuzzy Mode and Nearest Neighbour Hierarchical spatial clustering (NNH). Then the spots with the highest crime rates of drug smuggling for one province in Iran with borderline with Afghanistan are obtained. We will show that among these three methods NNH leads to the best result.

Keywords: GIS, Hot spots, nearest neighbor hierarchical spatial clustering, NNH, spatial analysis of crime

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Authors: M. M. Atashi, P. Malekzadeh

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A first known formulation for the out-of-plane free vibration analysis of functionally graded (FG) circular curved beams in thermal environment and with temperature dependent material properties is presented. The formulation is based on the first order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be temperature dependent and graded in the direction normal to the plane of the beam curvature. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle. Differential quadrature method (DQM), as an efficient and accurate numerical method, is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The fast rate of convergence of the method is investigated and the formulations are validated by comparing the results in the limit cases with the available solutions in the literature for isotropic circular curved beams. In addition, for FG circular curved beams with soft simply supported edges, the results are compared with the obtained exact solutions. Then, the effects of temperature rise, boundary conditions, material and geometrical parameters on the natural frequencies are investigated.

Keywords: out of plane, free vibration, curved beams, functionally graded, thermal environment

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Seyed Sadegh Naseralavi, Sadegh Balaghi, Ehsan Khojastehfar

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Time history dynamic analysis of structures is considered as an exact method while being computationally intensive. Filtration of earthquake strong ground motions applying wavelet transform is an approach towards reduction of computational efforts, particularly in optimization of structures against seismic effects. Wavelet transforms are categorized into continuum and discrete transforms. Since earthquake strong ground motion is a discrete function, the discrete wavelet transform is applied in the present paper. Wavelet transform reduces analysis time by filtration of non-effective frequencies of strong ground motion. Filtration process may be repeated several times while the approximation induces more errors. In this paper, strong ground motion of earthquake has been filtered once applying each wavelet. Strong ground motion of Northridge earthquake is filtered applying various wavelets and dynamic analysis of sampled shear and moment frames is implemented. The error, regarding application of each wavelet, is computed based on comparison of dynamic response of sampled structures with exact responses. Exact responses are computed by dynamic analysis of structures applying non-filtered strong ground motion.

Keywords: wavelet transform, computational error, computational duration, strong ground motion data

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Authors: Jeries J. Abou-Hanna, Bradley Storm

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This paper looks to reduce the complexity of determining stress intensity factors while maintaining high levels of accuracy by the use of a linearized layering approach. Many techniques for stress intensity factor determination exist, but they can be limited by conservative results, requiring too many user parameters, or by being too computationally intensive. Multiple notch geometries with various crack lengths were investigated in this study to better understand the effectiveness of the proposed method. By linearizing the average stresses in radial layers around the crack tip, stress intensity factors were found to have error ranging from -10.03% to 8.94% when compared to analytically exact solutions. This approach proved to be a robust and efficient method of accurately determining stress intensity factors.

Keywords: fracture mechanics, finite element method, stress intensity factor, stress linearization

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