Search results for: trend equations

Authors: Feng Yang

Abstract:

Machine learning (ML), especially deep learning (DL), has been extensively applied to many applications in recently years and gained great success in solving different problems, including scientific problems. However, conventional ML/DL methodologies are purely data-driven which have the limitations, such as need of ample amount of labelled training data, lack of consistency to physical principles, and lack of generalizability to new problems/domains. Recently, there is a growing consensus that ML models need to further take advantage of prior knowledge to deal with these limitations. Physics-informed machine learning, aiming at integration of physics/domain knowledge into ML, has been recognized as an emerging area of research, especially in the recent 2 to 3 years. In this work, physics-informed ML, specifically physics-informed neural network (NN), is employed and implemented to estimate the displacements at x, y, z directions in a solid mechanics problem that is controlled by equilibrium equations with boundary conditions. By incorporating the physics (i.e. the equilibrium equations) into the learning process of NN, it is showed that the NN can be trained very efficiently with a small set of labelled training data. Experiments with different settings of the NN model and the amount of labelled training data were conducted, and the results show that very high accuracy can be achieved in fulfilling the equilibrium equations as well as in predicting the displacements, e.g. in setting the overall displacement of 0.1, a root mean square error (RMSE) of 2.09 × 10−4 was achieved.

Keywords: deep learning, neural network, physics-informed machine learning, solid mechanics

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Authors: Guillermo Manuel Flores Figueroa, Juan Alejandro Vazquez Feijoo, Jose Navarro Antonio

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A continuous nonlinear system response may be obtained by an infinite sum of the so-called Volterra operators. Each operator is obtained from multidimensional convolution of nth-order between the nth-order Volterra kernel and the system input. These operators can also be obtained from the Associated Linear Equations (ALEs) that are linear models of subsystems which inputs and outputs are of the same nth-order. Each ALEs produces a particular nth-Volterra operator. As linear models a unitary impulse response can be obtained from them. This work shows the relationship between this unitary impulse responses and the corresponding order Volterra kernel.

Keywords: Volterra series, frequency response functions FRF, associated linear equations ALEs, unitary response function, Voterra kernel

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation

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Authors: Abdi Ammar, Ouazir Youcef, Laissaoui Abdelmalek

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In this work, an approach based on transmission lines theory is presented. It is exploited for the calculation of overvoltage created by direct impacts of lightning waves on a guard cable of an overhead high-voltage line. First, we show the theoretical developments leading to the propagation equation, its discretization by finite difference time domain method (FDTD), and the resulting linear algebraic equations, followed by the calculation of the linear parameters of the line. The second step consists of solving the transmission lines system of equations by the FDTD method. This enabled us to determine the spatio-temporal evolution of the induced overvoltage.

Keywords: lightning surge, transient overvoltage, eddy current, FDTD, electromagnetic compatibility, ground wire

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Authors: M. M. Atashi, P. Malekzadeh

Abstract:

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: Edward J. Kansa, Pavel Holoborodko

Abstract:

Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

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Authors: Elena M. Kopteva, Pavlina Jaluvkova, Zdenek Stuchlik

Abstract:

In spite of the numerous attempts to close the discussion about the influence of cosmological expansion on local gravitationally bounded systems, this question arises in literature again and again and remains still far from its final resolution. Here one of the main problems is the problem of obtaining a physically adequate model of strongly gravitating object immersed in non-static cosmological background. Such objects are usually called ‘cosmological’ black holes and are of great interest in wide set of cosmological and astrophysical areas. In this work the set of new exact solutions of the Einstein equations is derived for the flat space that generalizes the known Lemaitre-Tolman-Bondi solution for the case of nonzero pressure. The solutions obtained are pretending to describe the black hole immersed in nonstatic cosmological background and give a possibility to investigate the hot problems concerning the effects of the cosmological expansion in gravitationally bounded systems, the structure formation in the early universe, black hole thermodynamics and other related problems. It is shown that each of the solutions obtained contains either the Reissner-Nordstrom or the Schwarzschild black hole in the central region of the space. It is demonstrated that the approach of the mass function use in solving of the Einstein equations allows clear physical interpretation of the resulting solutions, that is of much benefit to any their concrete application.

Keywords: exact solutions of the Einstein equations, cosmological black holes, generalized Lemaitre-Tolman-Bondi solutions, nonzero pressure

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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

Abstract:

The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge-Kutta solution using 38 time steps.

Keywords: impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision

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Authors: E. Keramaris, V. Kanakoudis

Abstract:

In this study the water flow in an open channel over a sharp-crested weir is investigated experimentally. For this reason a series of laboratory experiments were performed in an open channel with a sharp-crested weir. The maximum head expected over the weir, the total upstream water height and the downstream water height of the impact in the constant bed of the open channel were measured. The discharge was measured using a tank put right after the open channel. In addition, the discharge and the upstream velocity were also calculated using already known equations. The main finding is that the relative error percentage for the majority of the experimental measurements is ± 4%, meaning that the calculation of the discharge with a sharp-crested weir gives very good results compared to the numerical results from known equations.

Keywords: sharp-crested weir, weir height, flow measurement, open channel flow

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Authors: Zhan Fengmei Yao, Hui Li, Jiahua Zhang

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The Northeast China (NEC) was the most important agriculture areas and known as the Golden-Maize-Belt. Based on observed crop data and crop model, we design four simulating experiments and separate relative impacts and contribution under climate change, planting date shift, and varieties change as well change of varieties and planting date. Without planting date and varieties change, maize yields had no significant change trend at Hailun station located in the north of NEC, and presented significant decrease by 0.2-0.4 t/10a at two stations, which located in the middle and the south of NEC. With planting date change, yields showed a significant increase by 0.09 - 0.47 t/10a. With varieties change, maize yields had significant increase by 1.8~ 1.9 t/10a at Hailun and Huadian stations, but a non-significant and low increase by 0.2t /10a at Benxi located in the south of NEC. With change of varieties and planting date, yields presented a significant increasing by 0.53-2.0 t/10a. Their contribution to yields was -25% ~ -55% for climate change, 15% ~ 35% for planting date change, and 20% ~110% for varieties change as well 30% ~135% for varieties with planting date shift. It found that change in varieties and planting date were highest yields and were responsible for significant increases in maize yields, varieties was secondly, and planting date was thirdly. It found that adaptation in varieties and planting date greatly improved maize yields, and increased yields annual variability. The increase of contribution with planting date and varieties change in 2000s was lower than in 1990s. Yields with the varieties change and yields with planting date and varieties change all showed a decreasing trend at Huadian and Benxi since 2002 or so. It indicated that maize yields increasing trend stagnated in the middle and south of NEC, and continued in the north of NEC.

Keywords: climate change, maize yields, varieties, planting date, impacts

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Authors: Dmitry V. Fomichev, Vladimir V. Solonin

Abstract:

This paper presents the findings from a numerical simulation of the flow in 37-rod fuel assembly models spaced by a double-wire trapezoidal wrapping as applied to the BREST-OD-300 experimental nuclear reactor. Data on a high static pressure distribution within the models, and equations for determining the fuel bundle flow friction factors have been obtained. Recommendations are provided on using the closing turbulence models available in the ANSYS Fluent. A comparative analysis has been performed against the existing empirical equations for determining the flow friction factors. The calculated and experimental data fit has been shown. An analysis into the experimental data and results of the numerical simulation of the BREST-OD-300 fuel rod assembly hydrodynamic performance are presented.

Keywords: BREST-OD-300, ware-spaces, fuel assembly, computation fluid dynamics

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Authors: Sandeep Singh

Abstract:

In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Aigul Manapova

Abstract:

We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: Radoslaw Pytlak, Damian Suski

Abstract:

The aim of the paper is to provide a computational tool for planning a haemodialysis process. It is shown that optimization methods can be used to obtain the most effective treatment focused on removing both urea and phosphorus during the process. In order to achieve that, the IV–compartment model of phosphorus kinetics is applied. This kinetics model takes into account a rebound phenomenon that can occur during haemodialysis and results in a hybrid model of the process. Furthermore, vector fields associated with the model equations are such that it is very likely that using the most intuitive objective functions in the planning problem could lead to solutions which include sliding motions. Therefore, building computational tools for solving the problem of planning a haemodialysis process has required constructing numerical algorithms for solving optimal control problems with hybrid systems. The paper concentrates on minimum time control of hybrid systems since this control objective is the most suitable for the haemodialysis process considered in the paper. The presented approach to optimal control problems with hybrid systems is different from the others in several aspects. First of all, it is assumed that a hybrid system can exhibit sliding modes. Secondly, the system’s motion on the switching surface is described by index 2 differential–algebraic equations, and that guarantees accurate tracking of the sliding motion surface. Thirdly, the gradients of the problem’s functionals are evaluated with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion and exhibit jump conditions at transition times. The optimality conditions in the form of the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding modes and with piecewise constant controls are stated. The presented sensitivity analysis can be used to construct globally convergent algorithms for solving considered problems. The paper presents numerical results of solving the haemodialysis planning problem.

Keywords: haemodialysis planning process, hybrid systems, optimal control, sliding motion

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

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

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

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Authors: D. Pradeep Mitra, Prafulla

Abstract:

Looking to the word propellant-less system it makes us to believe that it is an impossible one, but this paper demonstrates the use of microwaves to create a system which makes impossible to be possible, it means a propellant-less propulsion system using microwaves. In these thrusters, microwaves are radiated into a sealed parabolic cavity through a waveguide, which act on the surface of the cavity and follow the axis of the thrusters to produce thrust. The advantages of these thrusters are: (1) Producing thrust without propellant; without erosion, wear, and thermal stress from the hot exhaust gas; and at the same time increasing quality. (2) If the microwave output power is stable, the performance of thrusters is not affected by its working environment. This paper is demonstrated from general maxwell equations. These equations are used to create the mathematical model of the thrusters. These mathematical model helps us to calculate the Q factor and calculate the approximate thrust which would be generated in the system.

Keywords: propellant less, microwaves, parabolic wave guide, propulsion system

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Authors: Shyh Ming Chern

Abstract:

Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and, reasonable accuracy are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, They often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: equation of state, EoS, supercritical water, SCW

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Authors: Zia Ullah, Ruh Ullah

Abstract:

A research study was conceded in four locations (Swat, Dir, Kakul and Balakot) of Khyber Pakhtunkhwa, to find agro-climatic classes by using aridity index, Growing Degree Days of wheat and maize, crop growth index and Spatio-temporal analysis of rainfall by using long term climatic data (1970-2010). The climatic data used for research was acquired from Pakistan Meteorological Department (PMD) Islamabad, Agriculture Research Institute, Weather Station Peshawar and Tarnab Peshawar. Agro-climatic classes of each location were determined using three criteria mean temperature of the coldest month, mean temperature of the warmest month and aridity index. The agro-climatic classes of Dir, Swat, Kakul and Balakot were classified as Humid, Cold and very Warm (H-K-VW). Average aridity index of wheat for Dir, Swat, Kakul, and Balakot was 2.23, 2.67, 1.94 and 2.34 and for Maize was 1.31, 1.26, 1.97, and 2.83 respectively. The overall and decade-wise trend of GDD of Wheat and Maize was declined in Swat and Kakul while increased in Dir and Balakot.The average maximum CGI (1.26) and (0.73) of Wheat and Maize was observed for Balakot and Dir, while the minimum (1.09) and (0.62) was observed for Swat and Kakul. Spatio-temporal analysis of rainfall shows that the trend has increased in Swat while decreased in Dir, Kakul and Balakot. From the relation between rainfalls with altitude showed that there was an increasing trend between rainfalls with altitude. The maximum average rainfall was in Swat (2703mm) on altitude 2000m while the minimum average rainfall was observed in Kakul (1410mm) on altitude of 1255m.

Keywords: agro-climatic zones, aridity index, GDD, rainfall

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Authors: Hakan Aydogan, Fatih Bozkurt, Huseyin Coskun

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In this study, the signal of brain electrical activities of the sixteen students selected from the Department of Electrical and Energy at Usak University have been recorded during a lecturer performed happiness emotions for the first group and anger emotions for the second group in different time while the groups were in the classroom separately. The attention and meditation data extracted from the recorded signals have been analyzed and evaluated toward the teacher’s specific emotion states simultaneously. Attention levels of students who are under influence of happiness emotions of the lecturer have a positive trend and attention levels of students who are under influence of anger emotions of the lecturer have a negative trend. The meditation or mental relaxation levels of students who are under influence of happiness emotions of the lecturer are 34.3% higher comparing with the mental relaxation levels of students who are under influence of anger emotions of the lecturer.

Keywords: brainwave, attention, meditation, education

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Authors: Abdulatif Abdusalam, Mohamed Shaban

Abstract:

In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: I. Made Gatot Karohika, Shigeyuki Haruyama, Ken Kaminishi, Oke Oktavianty, Didik Nurhadiyanto

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Contact width and contact stress are important parameters related to the leakage behavior of corrugated metal gasket. In this study, contact width and contact stress of three-layer corrugated metal gasket are investigated due to the modulus of elasticity and thickness of surface layer for 2 type gasket (0-MPa and 400-MPa mode). A finite element method was employed to develop simulation solution to analysis the effect of each parameter. The result indicated that lowering the modulus of elasticity ratio of surface layer will result in better contact width but the average contact stresses are smaller. When the modulus of elasticity ratio is held constant with thickness ratio increase, its contact width has an increscent trend otherwise the average contact stress has decreased trend.

Keywords: contact width, contact stress, layer, metal gasket, corrugated, simulation

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: exponentially shrinking sheet, magnetic field, mixed convection, suction

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Authors: Mahmoud Roushdi, Hany Mostafa, Khaled Kheireldin

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Sinai Peninsula and Suez Canal Corridor are promising and important economic regions in Egypt due to the unique location and development opportunities. Thus, the climate change impacts should be assessed over the mentioned area. Accordingly, this paper aims to assess the climate extreme indices in through the last 35 year over Sinai Peninsula and Suez Canal Corridor in addition to predict the climate extreme indices up to 2100. Present and future climate indices were analyzed with using different RCP scenarios 4.5 and 8.5 from 2010 until 2100 for Sinai Peninsula and Suez Canal Corridor. Furthermore, both CanESM and HadGEM2 global circulation models were used. The results indicate that the number of summer days is predicted to increase, on the other hand the frost days is predicted to decrease. Moreover, it is noted a slight positive trend for the percentile of wet and extremely days R95p and R99p for RCP4.5 and negative trend for RCP8.5.

Keywords: climate change, extreme indices, RCP, Sinai Peninsula

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

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Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: ground surface relief, method of integral equations, numerical method, electromagnetic

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Authors: Alex Fedoseyev

Abstract:

This study investigates a generalized hydrodynamic equation (GHE) simplified model for the simulation of turbulent flow over a two-dimensional backward-facing step (BFS) at Reynolds number Re=132000. The GHE were derived from the generalized Boltzmann equation (GBE). GBE was obtained by first principles from the chain of Bogolubov kinetic equations and considers particles of finite dimensions. The GHE has additional terms, temporal and spatial fluctuations, compared to the Navier-Stokes equations (NSE). These terms have a timescale multiplier τ, and the GHE becomes the NSE when $\tau$ is zero. The nondimensional τ is a product of the Reynolds number and the squared length scale ratio, τ=Re*(l/L)², where l is the apparent Kolmogorov length scale, and L is a hydrodynamic length scale. The BFS flow modeling results obtained by 2D calculations cannot match the experimental data for Re>450. One or two additional equations are required for the turbulence model to be added to the NSE, which typically has two to five parameters to be tuned for specific problems. It is shown that the GHE does not require an additional turbulence model, whereas the turbulent velocity results are in good agreement with the experimental results. A review of several studies on the simulation of flow over the BFS from 1980 to 2023 is provided. Most of these studies used different turbulence models when Re>1000. In this study, the 2D turbulent flow over a BFS with height H=L/3 (where L is the channel height) at Reynolds number Re=132000 was investigated using numerical solutions of the GHE (by a finite-element method) and compared to the solutions from the Navier-Stokes equations, k–ε turbulence model, and experimental results. The comparison included the velocity profiles at X/L=5.33 (near the end of the recirculation zone, available from the experiment), recirculation zone length, and velocity flow field. The mean velocity of NSE was obtained by averaging the solution over the number of time steps. The solution with a standard k −ε model shows a velocity profile at X/L=5.33, which has no backward flow. A standard k−ε model underpredicts the experimental recirculation zone length X/L=7.0∓0.5 by a substantial amount of 20-25%, and a more sophisticated turbulence model is needed for this problem. The obtained data confirm that the GHE results are in good agreement with the experimental results for turbulent flow over two-dimensional BFS. A turbulence model was not required in this case. The computations were stable. The solution time for the GHE is the same or less than that for the NSE and significantly less than that for the NSE with the turbulence model. The proposed approach was limited to 2D and only one Reynolds number. Further work will extend this approach to 3D flow and a higher Re.

Keywords: backward-facing step, comparison with experimental data, generalized hydrodynamic equations, separation, reattachment, turbulent flow

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Authors: Abedalbasit M. Abedalhafiz, Aman Kasawneh, Zyad Altahynah, Ahmad Okor

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The purpose of this study was to determine the construct validity of the morale sprit scale (MSS). Ninety faculty members from colleges of physical education at Jordanian universities were chosen to participate in this study. The design of this study was an ex-post facto. The MSS consists of (48) items that measure different dimensions of morale spirit among faculty members. Principle axis factoring with oblique rotation was utilized to uncover the underlying structure of the instrument. The findings revealed eight factor solution explaining (72.825%). Seven factors were accepted according to the conditions of accepting factors. The seven factors were named morale as reflection of faculty and department's administration, regulations and instructions, working environment and conditions, promotions and incentives and salaries, relations between the faculty member's, the trend toward the college and university, the trend toward self factors.

Keywords: Factorial validity, morale sprit, faculty members, Jordanian Universities

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Authors: Farzad Shirzad, Bohlol Alijani, Mehry Akbary, Mohammad Saligheh

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Climate change and global warming are very important issues today. The process of climate change, especially changes in temperature and precipitation, is the most important issue in the environmental sciences. Climate change means changing the averages in the long run. Iran is located in arid and semi-arid regions due to its proximity to the equator and its location in the subtropical high pressure zone. In this respect, the Hyrcanian forest is a green necklace between the Caspian Sea and the south of the Alborz mountain range. In the forty-third session of UNESCO, it was registered as the second natural heritage of Iran. Beech is one of the most important tree species and the most industrial species of Hyrcanian forests. In this research, using dendroclimatology, the width of the tree ring, and climatic data of temperature and precipitation from Shanderman meteorological station located in the study area, And non-parametric Mann-Kendall statistical method to investigate the trend of climate change over a time series of 202 years of growth ringsAnd Pearson statistical method was used to correlate the growth of "ring" growth rings of beech trees with climatic variables in the region. The results obtained from the time series of beech growth rings showed that the changes in beech growth rings had a downward and negative trend and were significant at the level of 5% and climate change occurred. The average minimum, medium, and maximum temperatures and evaporation in the growing season had an increasing trend, and the annual precipitation had a decreasing trend. Using Pearson method during fitting the correlation of diameter of growth rings with temperature, for the average in July, August, and September, the correlation is negative, and the average temperature in July, August, and September is negative, and for the average The average maximum temperature in February was correlation-positive and at the level of 95% was significant, and with precipitation, in June the correlation was at the level of 95% positive and significant.

Keywords: climate change, dendroclimatology, hyrcanian forest, beech

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