Search results for: extended Arrhenius equation.

Authors: H. Mohammadiun, A. Kianifar, A. Kargar

Abstract:

Nowadays, there is little information, concerning the heat shield systems, and this information is not completely reliable to use in so many cases. for example, the precise calculation cannot be done for various materials. In addition, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test. Hence, using numerical modeling program that calculates the surface recession rate and interior temperature distribution is necessary. Also, numerical solution of governing equation for non-charring material ablation is presented in order to anticipate the recession rate and the heat response of non-charring heat shields. the governing equation is nonlinear and the Newton- Rafson method along with TDMA algorithm is used to solve this nonlinear equation system. Using Newton- Rafson method for solving the governing equation is one of the advantages of the solving method because this method is simple and it can be easily generalized to more difficult problems. The obtained results compared with reliable sources in order to examine the accuracy of compiling code.

Keywords: Ablation rate, surface recession, interior temperaturedistribution, non charring material ablation, Newton Rafson method.

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Authors: Chuanjian Wang, Changfu Liu, Zhengde Dai

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In this paper, the direct AnsAz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for each of the three-wave solutions. Mechanical features of resonance interaction among the multi-wave are discussed. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

Keywords: EKdV equation, Breather, Soliton, Bilinear form, The direct AnsAz method.

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Authors: Mohd.F.Shabir, P. Tamilporai, B. Rajendra Prasath

Abstract:

The fundamental aim of extended expansion concept is to achieve higher work done which in turn leads to higher thermal efficiency. This concept is compatible with the application of turbocharger and LHR engine. The Low Heat Rejection engine was developed by coating the piston crown, cylinder head inside with valves and cylinder liner with partially stabilized zirconia coating of 0.5 mm thickness. Extended expansion in diesel engines is termed as Miller cycle in which the expansion ratio is increased by reducing the compression ratio by modifying the inlet cam for late inlet valve closing. The specific fuel consumption reduces to an appreciable level and the thermal efficiency of the extended expansion turbocharged LHR engine is improved. In this work, a thermodynamic model was formulated and developed to simulate the LHR based extended expansion turbocharged direct injection diesel engine. It includes a gas flow model, a heat transfer model, and a two zone combustion model. Gas exchange model is modified by incorporating the Miller cycle, by delaying inlet valve closing timing which had resulted in considerable improvement in thermal efficiency of turbocharged LHR engines. The heat transfer model, calculates the convective and radiative heat transfer between the gas and wall by taking into account of the combustion chamber surface temperature swings. Using the two-zone combustion model, the combustion parameters and the chemical equilibrium compositions were determined. The chemical equilibrium compositions were used to calculate the Nitric oxide formation rate by assuming a modified Zeldovich mechanism. The accuracy of this model is scrutinized against actual test results from the engine. The factors which affect thermal efficiency and exhaust emissions were deduced and their influences were discussed. In the final analysis it is seen that there is an excellent agreement in all of these evaluations.

Keywords: Low Heat Rejection, Miller cycle.

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Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

Abstract:

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Raisa Kh. Bolotnova, Marat N. Galimzianov, Andrey S. Topolnikov, Uliana O. Agisheva, Valeria A. Buzina

Abstract:

The paper presents the results of theoretical and numerical modeling of propagation of shock waves in bubbly liquids related to nonlinear effects (realistic equation of state, chemical reactions, two-dimensional effects). On the basis on the Rankine- Hugoniot equations the problem of determination of parameters of passing and reflected shock waves in gas-liquid medium for isothermal, adiabatic and shock compression of the gas component is solved by using the wide-range equation of state of water in the analitic form. The phenomenon of shock wave intensification is investigated in the channel of variable cross section for the propagation of a shock wave in the liquid filled with bubbles containing chemically active gases. The results of modeling of the wave impulse impact on the solid wall covered with bubble layer are presented.

Keywords: bubbly liquid, cavitation, equation of state, shock wave

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Authors: Nopparat Pochai, Rujira Deepana

Abstract:

Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Functionally Graded Beam, Free Vibration, Elastic Foundation, Engesser-Timoshenko Beam Theory.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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Authors: Huei-Fu Lu

Abstract:

This study links up the theories of social psychology, economics and sport management to assess the impact of sport participation on subjective well-being (SWB) and use a simple statistic method to estimate the relative monetary value that sport participation derives SWB for Taiwan-s college students. By constructing proper measurements on sport participation and SWB respectively, a structural equation model (SEM) is developed to perform a confirmatory factory analysis, and the causal relationship between sport participation and SWB as well as the effect of the demographic variables on these two concepts are also discussed.

Keywords: Demographics, Economic value, Sport participation, Structural equation modeling (SEM), Subjective well-being.

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Authors: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional G-Brownian motion, Taylor’s series of fractional order, uncertain volatility.

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Authors: Fatma Ghangir, Andrzej F. Nowakowski, Franck C. G. A. Nicolleau, Thomas M. Michelitsch

Abstract:

The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.

Keywords: Multiphase flow, gas-liquid flow, Godunov schems, Riemann solvers, HLL scheme, HLLC scheme.

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

Abstract:

Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.

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Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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Authors: Gheorghe Galben, Daniel N. Aloi

Abstract:

Recently, the Spherical Motion Models (SMM-s) have been introduced [1]. These new models have been developed for 3D local landmark-base Autonomous Navigation (AN). This paper is revealing new arguments and experimental results to support the SMM-s characteristics. The accuracy and the robustness in performing a specific task are the main concerns of the new investigations. To analyze their performances of the SMM-s, the most powerful tools of estimation theory, the extended Kalman filter (EKF) and unscented Kalman filter (UKF), which give the best estimations in noisy environments, have been employed. The Monte Carlo validation implementations used to test the stability and robustness of the models have been employed as well.

Keywords: Autonomous navigation, extended kalman filter, unscented kalman filter, localization algorithms.

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Authors: R. Simutis, V. Galvanauskas, D. Levisauskas, J. Repsyte, V. Grincas

Abstract:

This paper deals with advanced state estimation algorithms for estimation of biomass concentration and specific growth rate in a typical fed-batch biotechnological process. This biotechnological process was represented by a nonlinear mass-balance based process model. Extended Kalman Filter (EKF) and Particle Filter (PF) was used to estimate the unmeasured state variables from oxygen uptake rate (OUR) and base consumption (BC) measurements. To obtain more general results, a simplified process model was involved in EKF and PF estimation algorithms. This model doesn’t require any special growth kinetic equations and could be applied for state estimation in various bioprocesses. The focus of this investigation was concentrated on the comparison of the estimation quality of the EKF and PF estimators by applying different measurement noises. The simulation results show that Particle Filter algorithm requires significantly more computation time for state estimation but gives lower estimation errors both for biomass concentration and specific growth rate. Also the tuning procedure for Particle Filter is simpler than for EKF. Consequently, Particle Filter should be preferred in real applications, especially for monitoring of industrial bioprocesses where the simplified implementation procedures are always desirable.

Keywords: Biomass concentration, Extended Kalman Filter, Particle Filter, State estimation, Specific growth rate.

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Authors: Azizollah Khormali, Seyyed Shahab Tabatabaee Moradi, Dmitry Petrakov

Abstract:

One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

Keywords: Explicit solution, Numerical simulation, Petroleum reservoir, Pressure distribution.

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Authors: F. Soleymani, M. Sharifi

Abstract:

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: A.Tajaddini

Abstract:

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

Abstract:

In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

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Authors: Nopparat Pochai

Abstract:

Smoke discharging is a main reason of air pollution problem from industrial plants. The obstacle of a building has an affect with the air pollutant discharge. In this research, a mathematical model of the smoke dispersion from two sources and one source with a structural obstacle is considered. The governing equation of the model is an isothermal mass transfer model in a viscous fluid. The finite element method is used to approximate the solutions of the model. The triangular linear elements have been used for discretising the domain, and time integration has been carried out by semi-implicit finite difference method. The simulations of smoke dispersion in cases of one chimney and two chimneys are presented. The maximum calculated smoke concentration of both cases are compared. It is then used to make the decision for smoke discharging and air pollutant control problems on industrial area.

Keywords: Air pollution, Smoke dispersion, Finite element method, Stream function, Vorticity equation, Convection-diffusion equation, Semi-implicit method

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Authors: L.A du Plessis

Abstract:

South Africa is facing a crisis with not being able to produce enough graduates in the scarce skills areas to sustain economic growth. The crisis is fuelled by a school system that does not produce enough potential students with Mathematics, Accounting and Science. Since the introduction of the new school curriculum in 2008, there is no longer an option to take pure maths on a standard grade level. Instead, only two mathematical subjects are offered: pure maths (which is on par with higher grade maths) and mathematical literacy. It is compulsory to take one or the other. As a result, lees student finishes Grade 12 with pure mathematics every year. This national problem needs urgent attention if South Africa is to make any headway in critical skills development as mathematics is a gateway to scarce skills professions. Higher education institutions initiated several initiatives in an attempt to address the above, including preparatory courses, bridging programmes and extended curricula with foundation provisions. In view of the above, and government policy directives to broaden access in the scarce skills areas to increase student throughput, foundation provision was introduced for Commerce and Information Technology programmes at the Vaal Triangle Campus (VTC) of North-West University (NWU) in 2010. Students enrolling for extended programmes do not comply with the minimum prerequisites for the normal programmes. The question then arises as to whether these programmes have the intended impact? This paper reports the results of a two year longitudinal study, tracking the first year academic achievement of the two cohorts of enrolments since 2010. The results provide valuable insight into the structuring of an extended programme and its potential impact.

Keywords: Access, extended programmes, foundation provision, mathematics.

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Authors: Shuzhen Yao, Fengjing Zhao, Jianwei He

Abstract:

The UML modeling of complex distributed systems often is a great challenge due to the large amount of parallel real-time operating components. In this paper the problems of verification of such systems are discussed. ECPN, an Extended Colored Petri Net is defined to formally describe state transitions of components and interactions among components. The relationship between sequence diagrams and Free Choice Petri Nets is investigated. Free Choice Petri Net theory helps verifying the liveness of sequence diagrams. By converting sequence diagrams to ECPNs and then comparing behaviors of sequence diagram ECPNs and statecharts, the consistency among models is analyzed. Finally, a verification process for an example model is demonstrated.

Keywords: Consistency, liveness, Petri Net, sequence diagram.

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Authors: ML. Benmessaoud, A. Lamrani, K. Nemra, AK. Souici

Abstract:

This paper presents an Extended Kaman Filter implementation of a single-camera Visual Simultaneous Localization and Mapping algorithm, a novel algorithm for simultaneous localization and mapping problem widely studied in mobile robotics field. The algorithm is vision and odometry-based, The odometry data is incremental, and therefore it will accumulate error over time, since the robot may slip or may be lifted, consequently if the odometry is used alone we can not accurately estimate the robot position, in this paper we show that a combination of odometry and visual landmark via the extended Kalman filter can improve the robot position estimate. We use a Pioneer II robot and motorized pan tilt camera models to implement the algorithm.

Keywords: Mobile Robot, Navigation, vSLAM, EKF, monocular.

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Authors: Hossein Sahoolizadeh, Davood Sarikhanimoghadam, Hamid Dehghani

Abstract:

This paper proposes new hybrid approaches for face recognition. Gabor wavelets representation of face images is an effective approach for both facial action recognition and face identification. Perform dimensionality reduction and linear discriminate analysis on the down sampled Gabor wavelet faces can increase the discriminate ability. Nearest feature space is extended to various similarity measures. In our experiments, proposed Gabor wavelet faces combined with extended neural net feature space classifier shows very good performance, which can achieve 93 % maximum correct recognition rate on ORL data set without any preprocessing step.

Keywords: Face detection, Neural Networks, Multi-layer Perceptron, Gabor wavelets.

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Authors: Marziyeh Halimi, Roushanak Lotfikar, Simin Mansouri Borojeni

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In this paper we considered the Neumann problem for the fourth order differential equation. First we define the weighted Sobolev space 2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution, as well as give the description of the spectrum and of the domain of definition of the corresponding operator.

Keywords: Neumann problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators.2000 mathematic subject classification: 34A05, 34A30.

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Authors: H. Taheri Shahraiyni, B. Ataie Ashtiani

Abstract:

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of different approximations of moisture capacity function, convergence criteria and time stepping methods were evaluated. Two different infiltration problems were solved to investigate the performance of different schemes. These problems include of vertical water flow in a wet and very dry soils. The numerical solutions of two problems were compared using four evaluation criteria and the results of comparisons showed that fully implicit scheme is better than the other schemes. In addition, utilizing of standard chord slope method for approximation of moisture capacity function, automatic time stepping method and difference between two successive iterations as convergence criterion in the fully implicit scheme can lead to better and more reliable results for simulation of fluid movement in different unsaturated soils.

Keywords: Finite Difference methods, Richards equation, fullyimplicit, Crank-Nicolson, Runge-Kutta.

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Authors: Z. El Felsoufi, L. Azrar

Abstract:

This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.

Keywords: Chimney, BEM and integral equation formulation, non uniform cross section, vibration and Flutter.

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