Search results for: Chapman Kolmogorov forward differential equations

Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Esmaeil Bahmyari

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The natural frequency analysis of the functionally graded (FG) rotating cylindrical shells subjected to thermal loads is studied based on the three-dimensional elasticity theory. The temperature-dependent assumption of the material properties is graded in the thickness direction, which varies based on the simple power law distribution. The governing equations and the appropriate boundary conditions, which include the effects of initial thermal stresses, are derived employing Hamilton’s principle. The initial thermo-mechanical stresses are obtained by the thermo-elastic equilibrium equation’s solution. As an efficient and accurate numerical tool, the differential quadrature method (DQM) is adopted to solve the thermo-elastic equilibrium equations, free vibration equations and natural frequencies are obtained. The high accuracy of the method is demonstrated by comparison studies with those existing solutions in the literature. Ultimately, the parametric studies are performed to demonstrate the effects of boundary conditions, temperature rise, material graded index, the thickness-to-length and the aspect ratios for the rotating cylindrical shells on the natural frequency.

Keywords: free vibration, DQM, elasticity theory, FG shell, rotating cylindrical shell

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Authors: A. Selmi

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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: differential transformation method, functionally graded material, mode shape, natural frequency

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Dávid Kovács, Bálint Csanády, Dániel Boros, Iván Ivkovic, Lóránt Nagy, Dalma Tóth-Lakits, László Márkus, András Lukács

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The modeling practice of financial instruments has seen significant change over the last decade due to the recognition of time-dependent and stochastically changing correlations among the market prices or the prices and market characteristics. To represent this phenomenon, the Stochastic Correlation Process (SCP) has come to the fore in the joint modeling of prices, offering a more nuanced description of their interdependence. This approach has allowed for the attainment of realistic tail dependencies, highlighting that prices tend to synchronize more during intense or volatile trading periods, resulting in stronger correlations. Evidence in statistical literature suggests that, similarly to the volatility, the SCP of certain stock prices follows rough paths, which can be described using fractional differential equations. However, estimating parameters for these equations often involves complex and computation-intensive algorithms, creating a necessity for alternative solutions. In this regard, the Fractional Ornstein-Uhlenbeck (fOU) process from the family of fractional processes offers a promising path. We can effectively describe the rough SCP by utilizing certain transformations of the fOU. We employed neural networks to understand the behavior of these processes. We had to develop a fast algorithm to generate a valid and suitably large sample from the appropriate process to train the network. With an extensive training set, the neural network can estimate the process parameters accurately and efficiently. Although the initial focus was the fOU, the resulting model displayed broader applicability, thus paving the way for further investigation of other processes in the realm of financial mathematics. The utility of SCP extends beyond its immediate application. It also serves as a springboard for a deeper exploration of fractional processes and for extending existing models that use ordinary Wiener processes to fractional scenarios. In essence, deploying both SCP and fractional processes in financial models provides new, more accurate ways to depict market dynamics.

Keywords: fractional Ornstein-Uhlenbeck process, fractional stochastic processes, Heston model, neural networks, stochastic correlation, stochastic differential equations, stochastic volatility

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Authors: Tayeb Bensattalah, Mohamed Zidour, Mohamed Ait Amar Meziane, Tahar Hassaine Daouadji, Abdelouahed Tounsi

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In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Influence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated.

Keywords: boundary conditions, buckling, non-local, differential transform method

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Authors: Hesham A. Elkaranshawy, Amr Abdelrazek, Hosam Ezzat

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This paper analyzes a single point rough collision in three dimensional rigid-multibody systems. A set of nonlinear different equations describing the progress and outcome of the impact are obtained. Specifically in case of the tangential, referred to as sliding, component of impact velocity is of great importance. Numerical methods are used to solve this problem. In this work, all these possible sliding behaviors during impact are identified, conditions leading to each behavior are specified, and an appropriate numerical procedure is suggested. A case of a four-degrees-of-freedom spatial robot that collides with its environment is investigated. The phase portrait of the tangential velocity, which presents the flow trajectories for different initial conditions, is calculated. Using the coefficient of friction as a control parameter, few phase portraits are drawn, each for a specific value of this coefficient. In addition, the bifurcation associated with the variation of this coefficient will be investigated.

Keywords: friction impact, three-dimensional rigid multibody systems, sliding velocity, nonlinear ordinary differential equations, phase portrait

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Neda Dekamei, Mostafa Sarabzadeh, Masoumeh Bigdeli

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Backward running is commonly used in different sports conditioning, motor learning, and neurological purposes, and even more commonly in physical rehabilitation. The present study evaluated the effects of six weeks backward and forward running methods on balance promotion adaptation in students. 12 male and female preseniors with the age range of 45-60 years participated and were randomly classified into two groups of backward running (n: 6) and forward running (n: 6) training interventions. During six weeks, 3 sessions per week, all subjects underwent stated different models of backward and forward running training on treadmill (65-80 of HR max). Pre and post-tests were performed by force plate and electromyogram, two times before and after intervention. Data were analyzed using by T test. On the basis of obtained data, significant differences were recorded on balance and plantar flexion force in backward running (BR) and no difference for forward running (FR). It seems the training model of backward running can generate more stimulus to achieve better plantar flexion force and strengthening ankle protectors which leads to balance improvement in pre aging period. It can be recommended as an effective method to promote seniors life quality especially in balance neuromuscular parameters.

Keywords: backward running, balance, plantar flexion, pre seniors

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Authors: Ale M. O., Manuwa S. I., Olukunle O. J., Ewetumo T.

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Five varying speeds of 1.5, 1.8, 2.1, 2.3, and 2.6 km/h were used at a constant soil depth of 100 mm to determine the effects of forward speed on the draught requirement of a semi-automatic cassava planter under the pneumatic wheel and rigid wheel usage on a well prepared sandy clay loam soil. The soil draught was electronically measured using an on-the-go soil draught measuring instrumentation system developed for the purpose of this research. The results showed an exponential relationship between forward speed and draught, in which draught ranging between 24.91 and 744.44N increased with an increase in forward speed in the rigid wheel experiment. This is contrary to the polynomial relationship observed in the pneumatic wheel experiment in which the draught varied between 96.09 and 343.53 N. It was observed in the experiments that the optimum speed of 1.5 km/h had the least values of draught in both the pneumatic wheel and rigid wheel experiments, with higher values in the pneumatic experiment. It was generally noted that the rigid wheel planter with less value of draught requires less energy required for operation. It is therefore concluded that operating the semi-automatic cassava planter with rigid wheels will be more economical for cassava farmers than operating the planter with pneumatic wheels.

Keywords: Cassava planter, planting, forward speed, draught, wheel type

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Authors: Temur Chilachava

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In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two various widespread languages, taking into account demographic factor is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the population and government institutions with the widespread second language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the third population (probably small state formation, an autonomy), exposed to bilateral assimilation from two rather powerful states. Earlier by us it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimilated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model "predator - the victim", thus, naturally a role of the victim plays the population which has undergone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of assimilators in an initial time point) to the population of the first assimilator. In the second case the problem is actually reduced to nonlinear system of two differential equations describing type model "a predator – the victim", with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situations, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the population of the assimilating states.

Keywords: nonlinear mathematical model, bilateral assimilation, demographic factor, first integrals, result of assimilation, intervals of change of number of the population

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Authors: Utkan Caliskan

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Two types of numerical codes based on finite volume method are developed in order to solve compressible Euler equations to simulate the flow through forward facing step channel. Both algorithms have AUSM+- up (Advection Upstream Splitting Method) scheme for flux splitting and two-stage Runge-Kutta scheme for time stepping. In this study, the flux calculations differentiate between the algorithm based on OpenFOAM mesh format which is called 'face-based' algorithm and the basic algorithm which is called 'element-based' algorithm. The face-based algorithm avoids redundant flux computations and also is more flexible with hybrid grids. Moreover, some of OpenFOAM’s preprocessing utilities can be used on the mesh. Parallelization of the face based algorithm for which atomic operations are needed due to the shared memory model, is also presented. For several mesh sizes, 2.13x speed up is obtained with face-based approach over the element-based approach.

Keywords: cell centered finite volume method, compressible Euler equations, OpenFOAM mesh format, OpenMP

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Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

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Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: erodible beds, finite element method, finite volume method, nonlinear elasticity, shallow water equations, stresses in soil

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Alexander Blokhin, Ekaterina Kruglova, Boris Semisalov

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Mathematical model based on the mesoscopic theory of polymer dynamics is developed for numerical simulation of the flows of polymeric liquid between two coaxial cylinders. This model is a system of nonlinear partial differential equations written in the cylindrical coordinate system and coupled with the heat conduction equation including a specific dissipation term. The stationary flows similar to classical Poiseuille ones are considered, and the resolving equations for the velocity of flow and for the temperature are obtained. For solving them, a fast pseudospectral method is designed based on Chebyshev approximations, that enables one to simulate the flows through the channels with extremely small relative values of the radius of inner cylinder. The numerical analysis of the dependance of flow on this radius and on the values of dissipation constant is done.

Keywords: dynamics of polymeric liquid, heat dissipation, singularly perturbed problem, pseudospectral method, Chebyshev polynomials, stabilization technique

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Authors: Serdal Pamuk, Irem Cay

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Our model is based on the theory of reinforced random walks coupled with Michealis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived tumor angiogenesis factor (TAF) into proteolytic enzyme which in turn degrade the basal lamina. The model consists of two main parts. First part has seven differential equations (DE’s) in one space dimension over the capillary, whereas the second part has the same number of DE’s in two space dimensions in the extra cellular matrix (ECM). We connect these two parts via some boundary conditions to move the cells into the ECM in order to initiate capillary formation. But, when does this movement begin? To address this question we estimate the thresholds that activate the transport equations in the capillary. We do this by using steady-state analysis of TAF equation under some assumptions. Once these equations are activated endothelial, pericyte and macrophage cells begin to move into the ECM for the initiation of angiogenesis. We do believe that our results play an important role for the mechanisms of cell migration which are crucial for tumor angiogenesis. Furthermore, we estimate the long time tendency of these three cells, and find that they tend to the transition probability functions as time evolves. We provide our numerical solutions which are in good agreement with our theoretical results.

Keywords: angiogenesis, capillary formation, mathematical analysis, steady-state, transition probability function

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: P. C. Tewari, Parveen Kumar

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The paper describes the availability analysis of milling system of a rice milling plant using probabilistic approach. The subsystems under study are special purpose machines. The availability analysis of the system is carried out to determine the effect of failure and repair rates of each subsystem on overall performance (i.e. steady state availability) of system concerned. Further, on the basis of effect of repair rates on the system availability, maintenance repair priorities have been suggested. The problem is formulated using Markov Birth-Death process taking exponential distribution for probable failures and repair rates. The first order differential equations associated with transition diagram are developed by using mnemonic rule. These equations are solved using normalizing conditions and recursive method to drive out the steady state availability expression of the system. The findings of the paper are presented and discussed with the plant personnel to adopt a suitable maintenance policy to increase the productivity of the rice milling plant.

Keywords: availability modeling, Markov process, milling system, rice milling plant

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Authors: Yohannes Yirga, Daniel Tesfay

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The convective heat and mass transfer in nanofluid flow through a porous media due to a permeable stretching sheet with magnetic field, viscous dissipation, and chemical reaction and Soret effects are numerically investigated. Two types of nanofluids, namely Cu-water and Ag-water were studied. The governing boundary layer equations are formulated and reduced to a set of ordinary differential equations using similarity transformations and then solved numerically using the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier linearly stretching sheet problems in the literature.

Keywords: heat and mass transfer, magnetohydrodynamics, nanofluid, fluid dynamics

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Authors: F. Boudet, V. Galano, D. Gmira, L. Munoz, A. Reina

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Commodities pricing needs a specific approach as they are often linked to each other and so are expectedly doing their prices. They are called co-integrated when at least one stationary linear combination exists between them. Though widespread in economic literature, and even if many equilibrium relations and co-movements exist in the economy, this principle of co-movement is not developed in derivatives field. The present study focuses on the following problem: How can the price of a forward agreement on a commodity be simulated, when it is co-integrated with other ones? Theoretical analysis is developed from Gibson-Schwartz model and an analytical solution is given for short maturities contracts and under risk-neutral conditions. The application has been made to crude oil and heating oil energy commodities and result confirms the applicability of proposed method.

Keywords: co-integration, commodities, forward pricing, Gibson-Schwartz

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Authors: Cagri Mollamahmutoglu, Ali Mercan, Aykut Levent

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

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

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Authors: Vikas Kumar

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The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary layer equations involved in the problem to a system of non linear coupled differential equations. The solution of this system is obtained by using power series approximation. The flow characteristics i.e. radial, tangential, axial velocities and boundary layer displacement thickness are calculated for various values of MFD (magnetic field dependent) viscosity and for different values of suction injection parameter. Besides this, skin friction coefficients are also calculated on the surface of the disk. Thus, the obtained results are presented numerically and graphically in the paper.

Keywords: axi-symmetric, ferrofluid, magnetic field, porous rotating disk

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Authors: Safitri W. Nur, Prathisto Panuntun L. Unggul, M. Ivan Adi Perdana, R. Dary Wira Mahadika

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On soft soil areas, high embankment as a preloading needed to improve the bearing capacity of the soil. For sustainable development, the construction of embankment must not disturb the area around of them. So, the influence area must be known before the contractor applied their embankment design. For several cases in Indonesia, the area around of embankment construction is housing resident and other building. So that, the influence area must be identified to avoid the differential settlement occurs on the buildings around of them. Differential settlement causes the building crack. Each building has a limited tolerance for the differential settlement. For concrete buildings, the tolerance is 0,002 – 0,003 m and for steel buildings, the tolerance is 0,006 – 0,008 m. If the differential settlement stands on the range of that value, building crack can be avoided. In fact, the settlement around of embankment is assumed as zero. Because of that, so many problems happen when high embankment applied on soft soil area. This research used the superposition method combined with plaxis analysis to know the influences area around of embankment in some location with the differential characteristic of the soft soil. The undisturbed soil samples take on 55 locations with undisturbed soil samples at some soft soils location in Indonesia. Based on this research, it was concluded that the effects of embankment variation are if more gentle the slope, the influence area will be greater and vice versa. The largest of the influence area with h initial embankment equal to 2 - 6 m with slopes 1:1, 1:2, 1:3, 1:4, 1:5, 1:6, 1:7, 1:8 is 32 m from the edge of the embankment.

Keywords: differential settlement, embankment, influence area, slope, soft soil

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Authors: Mohammad Bakhshi, Firas Al Janabi

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High resolution rain data are very important to fulfill the input of hydrological models. Among models of high-resolution rainfall data generation, the temporal disaggregation was chosen for this study. The paper attempts to generate three different rainfall resolutions (4-hourly, hourly and 10-minutes) from daily for around 20-year record period. The process was done by DiMoN tool which is based on random cascade model and method of fragment. Differences between observed and simulated rain dataset are evaluated with variety of statistical and empirical methods: Kolmogorov-Smirnov test (K-S), usual statistics, and Exceedance probability. The tool worked well at preserving the daily rainfall values in wet days, however, the generated data are cumulated in a shorter time period and made stronger storms. It is demonstrated that the difference between generated and observed cumulative distribution function curve of 4-hourly datasets is passed the K-S test criteria while in hourly and 10-minutes datasets the P-value should be employed to prove that their differences were reasonable. The results are encouraging considering the overestimation of generated high-resolution rainfall data.

Keywords: DiMoN Tool, disaggregation, exceedance probability, Kolmogorov-Smirnov test, rainfall

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Authors: Mohamed Abdel-Monem, Gamal Sowilam, Omar Hegazy

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This paper presents a technical assessment of an electric vehicle with two independent rear-wheel motor and an improved traction control system. The electric differential and the control strategy have been implemented to assure that in a straight trajectory, the two rear-wheels run exactly at the same speed, considering the same/different road conditions under the left and right side of the wheels. In case of turning to right/left, the difference between the two rear-wheels speeds assures a vehicle trajectory without sliding, thanks to a harmony between the electric differential and the control strategy. The present article demonstrates a complete model and analysis of a traction control system, considering four different traction scenarios, for two independent rear-wheels motors for electric vehicles. Furthermore, the vehicle model, including wheel dynamics, load forces, electric differential, and control strategy, is designed and verified by using MATLAB/Simulink environment.

Keywords: electric vehicle, energy saving, multi-motor, electric differential, simulation and control

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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: Minas Balyan

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Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The purpose of this article is to analyze the finite displacement of Columns by applying the Modified Newmark Method. This research will be performed on Columns subjected to compressive axial load, therefore the non-linearity of the geometry is also considered. If the considered strut is perfect, the governing differential equation contains a branching point in the solution path. Investigation into the Elastica is a part of generalizing the developed method. It presents the ability of the Modified Newmark Method in treating non-linear differential equations Derived from elastic strut stability problems. These include not only an approximate polynomial solution for the Elastica problems, but can also recognize the branching point and the stable solution. However, this investigation deals with the post-buckling response of elastic and pin ended columns subjected to central or equally eccentric axial loads.

Keywords: columns, structural modeling, structures & structural stability, loads

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Authors: Shih-Kuei Lin

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The characterization of the arbitrage-free dynamics of interest rates is developed in this study under the presence of Markov jump risks, when the term structure of the interest rates is modeled through simple forward rates. We consider Markov jump risks by allowing randomness in jump sizes, independence between jump sizes and jump times. The Markov jump diffusion model is used to capture empirical phenomena and to accurately describe interest jump risks in a financial market. We derive the arbitrage-free model of simple forward rates under the spot measure. Moreover, the analytical pricing formulas for a cap and a floor are derived under the forward measure when the jump size follows a lognormal distribution. In our empirical analysis, we find that the LIBOR market model with Markov jump risk better accounts for changes from/to different states and different rates.

Keywords: arbitrage-free, cap and floor, Markov jump diffusion model, simple forward rate model, volatility smile, EM algorithm

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Authors: Kanpop Saion, Sakreya Chitwong

Abstract:

Control of superheated steam temperature in the steam generation is essential for the efficiency safety and increment age of the boiler. Conventional cascade PID temperature control in the super heater is known to be efficient to compensate disturbance. However, the complex of thermal power plant due to nonlinearity, load disturbance and time delay of steam of superheater system is bigger than other control systems. The cascade loop with feed forward steam temperature control with energy balance compensator using thermodynamic model has been used for the compensation the complex structure of superheater. In order to improve the performance of steam temperature control. The experiment is implemented for 100% load steady and load changing state. The cascade with feed forward with energy balance steam temperature control has stabilized the system as well.

Keywords: cascade with feed forward, boiler, superheated steam temperature control, enthalpy balance

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