Search results for: wave propagation equations.

Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

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: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.

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Authors: M. Ghanbari, S. Hossainpour, G. Rezazadeh

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In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model, the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.

Keywords: Micro-polar theory, Galerkin method, MEMS, micro-fluid.

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Authors: Fang Ye, Han Yu, Yibing Li

Abstract:

Radio interference is one of the major concerns in using the global positioning system (GPS) for civilian and military applications. Interference signals are produced not only through all electronic systems but also illegal jammers. Among different types of interferences, continuous wave (CW) interference has strong adverse impacts on the quality of the received signal. In this paper, we make more detailed analysis for CW interference effects on GPS signal quality. Based on the C/A code spectrum lines, the influence of CW interference on the acquisition performance of GPS receivers is further analysed. This influence is supported by simulation results using GPS software receiver. As the most important user parameter of GPS receivers, the mathematical expression of bit error probability is also derived in the presence of CW interference, and the expression is consistent with the Monte Carlo simulation results. The research on CW interference provides some theoretical gist and new thoughts on monitoring the radio noise environment and improving the anti-jamming ability of GPS receivers.

Keywords: GPS, CW interference, acquisition performance, bit error probability, Monte Carlo.

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Authors: Hans H. Diel

Abstract:

This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.

Keywords: Computational Modeling, Simulation of Quantum Theory, Quantum Field Theory, Quantum Electrodynamics

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Authors: Etsuo Morishita

Abstract:

In this paper, we show shallow water in a tin box as an analogous simulation tool for high-speed aerodynamics education and research. It is customary that we use a water tank to create shallow water flow. While a flow in a water tank is not necessarily uniform and is sometimes wavy, we can visualize a clear supercritical flow even when we move a body manually in stationary water in a simple shallow tin box. We can visualize a blunt shock wave around a moving circular cylinder together with a shock pattern around a diamond airfoil. Another interesting analogous experiment is a hydrodynamic shock tube with water and tea. We observe the contact surface clearly due to color difference of the two liquids those are invisible in the real gas dynamics experiment. We first revisit the similarities between high-speed aerodynamics and shallow water hydraulics. Several educational and research experiments are then introduced for engineering students. Shallow water experiments in a tin box simulate properly the high-speed flows.

Keywords: Aerodynamics compressible flow, gas dynamics, hydraulics, shock wave.

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

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Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: Azam Marjani, Saeed Shirazian

Abstract:

This work deals with modeling and simulation of SO2 removal in a ceramic membrane by means of FEM. A mass transfer model was developed to predict the performance of SO2 absorption in a chemical solvent. The model was based on solving conservation equations for gas component in the membrane. Computational fluid dynamics (CFD) of mass and momentum were used to solve the model equations. The simulations aimed to obtain the distribution of gas concentration in the absorption process. The effect of the operating parameters on the efficiency of the ceramic membrane was evaluated. The modeling findings showed that the gas phase velocity has significant effect on the removal of gas whereas the liquid phase does not affect the SO2 removal significantly. It is also indicated that the main mass transfer resistance is placed in the membrane and gas phase because of high tortuosity of the ceramic membrane.

Keywords: Gas separation, finite element, ceramic, sulphur dioxide, simulation.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, A. H. Usman

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Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.

Keywords: Option price valuation, Martingales, Partial Differential Equations, PDEs, Equivalent Martingale Measure, Girsanov Theorem, Feyman-Kac Theorem, European Put Option.

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Authors: V. Paployan, K. Madoyan, A. Melikyan, H. Minassian

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In this paper, we calculate the two-photon ionization (TPI) cross-section for pump-probe scheme in Ag neutral cluster. The pump photon energy is assumed to be close to the surface plasmon (SP) energy of cluster in dielectric media. Due to this choice, the pump wave excites collective oscillations of electrons-SP and the probe wave causes ionization of the cluster. Since the interband transition energy in Ag exceeds the SP resonance energy, the main contribution into the TPI comes from the latter. The advantage of Ag clusters as compared to the other noble metals is that the SP resonance in silver cluster is much sharper because of peculiarities of its dielectric function. The calculations are performed by separating the coordinates of electrons corresponding to the collective oscillations and the individual motion that allows taking into account the resonance contribution of excited SP oscillations. It is shown that the ionization cross section increases by two orders of magnitude if the energy of the pump photon matches the surface plasmon energy in the cluster.

Keywords: Resonance enhancement, silver clusters, surface plasmon, two-photon ionization.

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Authors: Joseph S. Ojo, Vincent A. Akpan, Oladayo G. Ajileye, Olalekan L, Ojo

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In this paper, the intelligent algorithm (IA) that is capable of adapting to dynamical tropical weather conditions is proposed based on fuzzy logic techniques. The IA effectively interacts with the quality of service (QoS) criteria irrespective of the dynamic tropical weather to achieve improvement in the satellite links. To achieve this, an adaptive network-based fuzzy inference system (ANFIS) has been adopted. The algorithm is capable of interacting with the weather fluctuation to generate appropriate improvement to the satellite QoS for efficient services to the customers. 5-year (2012-2016) rainfall rate of one-minute integration time series data has been used to derive fading based on ITU-R P. 618-12 propagation models. The data are obtained from the measurement undertaken by the Communication Research Group (CRG), Physics Department, Federal University of Technology, Akure, Nigeria. The rain attenuation and signal-to-noise ratio (SNR) were derived for frequency between Ku and V-band and propagation angle with respect to different transmitting power. The simulated results show a substantial reduction in SNR especially for application in the area of digital video broadcast-second generation coding modulation satellite networks.

Keywords: Fuzzy logic, intelligent algorithm, Nigeria, QoS, satellite applications, tropical weather.

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Authors: Ali Keshavarzi, Fereydoon Sarmadian

Abstract:

Investigation of soil properties like Cation Exchange Capacity (CEC) plays important roles in study of environmental reaserches as the spatial and temporal variability of this property have been led to development of indirect methods in estimation of this soil characteristic. Pedotransfer functions (PTFs) provide an alternative by estimating soil parameters from more readily available soil data. 70 soil samples were collected from different horizons of 15 soil profiles located in the Ziaran region, Qazvin province, Iran. Then, multivariate regression and neural network model (feedforward back propagation network) were employed to develop a pedotransfer function for predicting soil parameter using easily measurable characteristics of clay and organic carbon. The performance of the multivariate regression and neural network model was evaluated using a test data set. In order to evaluate the models, root mean square error (RMSE) was used. The value of RMSE and R2 derived by ANN model for CEC were 0.47 and 0.94 respectively, while these parameters for multivariate regression model were 0.65 and 0.88 respectively. Results showed that artificial neural network with seven neurons in hidden layer had better performance in predicting soil cation exchange capacity than multivariate regression.

Keywords: Easily measurable characteristics, Feed-forwardback propagation, Pedotransfer functions, CEC.

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid.

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Authors: Chun-Ta Chen, Te-Tan Liao, Hoang-Vuong Pham

Abstract:

In this paper motion analysis on a winding stair-climbing is investigated using our proposed rotational arm type of robotic wheelchair. For now, the robotic wheelchair is operated in an open mode to climb winding stairs by a dynamic turning, therefore, the dynamics model is required to ensure a passenger-s safety. Equations of motion based on the skid-steering analysis are developed for the trajectory planning and motion analysis on climbing winding stairs. Since the robotic wheelchair must climb a winding staircase stably, the winding trajectory becomes a constraint equation to be followed, and the Baumgarte-s method is used to solve for the constrained dynamics equations. Experimental results validate the behavior of the prototype as it climbs a winding stair.

Keywords: Climb, robotic wheelchair, skid-steering, windingstair .

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Authors: A. Bachrata, N. Marie, F. Bertrand, J. B. Droin

Abstract:

The in-depth understanding of severe accident propagation in Generation IV of nuclear reactors is important so that appropriate risk management can be undertaken early in their design process. This paper is focused on model improvements in the SIMMER code in order to perform studies of severe accident mitigation of Sodium Fast Reactor. During the design process of the mitigation devices dedicated to extraction of molten fuel from the core region, the molten fuel propagation from the core up to the core catcher has to be studied. In this aim, analytical as well as the complex thermohydraulic simulations with SIMMER-III code are performed. The studies presented in this paper focus on physical phenomena and associated physical models that influence the corium relocation. Firstly, the molten pool heat exchange with surrounding structures is analyzed since it influences directly the instant of rupture of the dedicated tubes favoring the corium relocation for mitigation purpose. After the corium penetration into mitigation tubes, the fuel-coolant interactions result in formation of debris bed. Analyses of debris bed fluidization as well as sinking into a fluid are presented in this paper.

Keywords: Corium, mitigation tubes, SIMMER-III, sodium fast reactor (SFR).

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Authors: Anupama Pande, Ashok Kumar Thakur, Swapnoneel Roy

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A complex valued neural network is a neural network which consists of complex valued input and/or weights and/or thresholds and/or activation functions. Complex-valued neural networks have been widening the scope of applications not only in electronics and informatics, but also in social systems. One of the most important applications of the complex valued neural network is in signal processing. In Neural networks, generalized mean neuron model (GMN) is often discussed and studied. The GMN includes a new aggregation function based on the concept of generalized mean of all the inputs to the neuron. This paper aims to present exhaustive results of using Generalized Mean Neuron model in a complex-valued neural network model that uses the back-propagation algorithm (called -Complex-BP-) for learning. Our experiments results demonstrate the effectiveness of a Generalized Mean Neuron Model in a complex plane for signal processing over a real valued neural network. We have studied and stated various observations like effect of learning rates, ranges of the initial weights randomly selected, error functions used and number of iterations for the convergence of error required on a Generalized Mean neural network model. Some inherent properties of this complex back propagation algorithm are also studied and discussed.

Keywords: Complex valued neural network, Generalized Meanneuron model, Signal processing.

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Authors: Mughal Yar M, Israr Ul Haq, Bushra Noman

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The stem cells have ability to differentiated themselves through mitotic cell division and various range of specialized cell types. Cellular differentiation is a way by which few specialized cell develops into more specialized.This paper studies the fundamental problem of computational schema for an artificial neural network based on chemical, physical and biological variables of state. By doing this type of study system could be model for a viable propagation of various economically important stem cells differentiation. This paper proposes various differentiation outcomes of artificial neural network into variety of potential specialized cells on implementing MATLAB version 2009. A feed-forward back propagation kind of network was created to input vector (five input elements) with single hidden layer and one output unit in output layer. The efficiency of neural network was done by the assessment of results achieved from this study with that of experimental data input and chosen target data. The propose solution for the efficiency of artificial neural network assessed by the comparatative analysis of “Mean Square Error" at zero epochs. There are different variables of data in order to test the targeted results.

Keywords: Computational shcmin, meiosis, mitosis, neuralnetwork, Stem cell SOM;

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Authors: Mihai Lungu

Abstract:

The paper presents the design of a mini-UAV attitude controller using the backstepping method. Starting from the nonlinear dynamic equations of the mini-UAV, by using the backstepping method, the author of this paper obtained the expressions of the elevator, rudder and aileron deflections, which stabilize the UAV, at each moment, to the desired values of the attitude angles. The attitude controller controls the attitude angles, the angular rates, the angular accelerations and other variables that describe the UAV longitudinal and lateral motions. To design the nonlinear controller, by using the backstepping technique, the nonlinear equations and the Lyapunov analysis have been directly used. The designed controller has been implemented in Matlab/Simulink environment and its effectiveness has been tested with a campaign of numerical simulations using data from the UAV flight tests. The obtained results are very good and they are better than the ones found in previous works.

Keywords: Attitude angles, Backstepping, Controller, UAV.

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Authors: Debajyoti Mishra, Urmila Bhanja

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In this paper, a novel fuzzy approach is developed while solving the Dynamic Routing and Wavelength Assignment (DRWA) problem in optical networks with Wavelength Division Multiplexing (WDM). In this work, the effect of nonlinear and linear impairments such as Four Wave Mixing (FWM) and amplifier spontaneous emission (ASE) noise are incorporated respectively. The novel algorithm incorporates fuzzy logic controller (FLC) to reduce the effect of FWM noise and ASE noise on a requested lightpath referred in this work as FWM aware fuzzy dynamic routing and wavelength assignment algorithm. The FWM crosstalk products and the static FWM noise power per link are pre computed in order to reduce the set up time of a requested lightpath, and stored in an offline database. These are retrieved during the setting up of a lightpath and evaluated online taking the dynamic parameters like cost of the links into consideration.

Keywords: Amplifier spontaneous emission (ASE), Dynamic routing and wavelength assignment, Four wave mixing (FWM), Fuzzy rule based system (FRBS).

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Authors: M. Govindarajan, R. M. Chandrasekaran

Abstract:

Text Mining is around applying knowledge discovery techniques to unstructured text is termed knowledge discovery in text (KDT), or Text data mining or Text Mining. In Neural Network that address classification problems, training set, testing set, learning rate are considered as key tasks. That is collection of input/output patterns that are used to train the network and used to assess the network performance, set the rate of adjustments. This paper describes a proposed back propagation neural net classifier that performs cross validation for original Neural Network. In order to reduce the optimization of classification accuracy, training time. The feasibility the benefits of the proposed approach are demonstrated by means of five data sets like contact-lenses, cpu, weather symbolic, Weather, labor-nega-data. It is shown that , compared to exiting neural network, the training time is reduced by more than 10 times faster when the dataset is larger than CPU or the network has many hidden units while accuracy ('percent correct') was the same for all datasets but contact-lences, which is the only one with missing attributes. For contact-lences the accuracy with Proposed Neural Network was in average around 0.3 % less than with the original Neural Network. This algorithm is independent of specify data sets so that many ideas and solutions can be transferred to other classifier paradigms.

Keywords: Back propagation, classification accuracy, textmining, time complexity.

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Authors: Osama A. Marzouk

Abstract:

We propose a reduced-ordermodel for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform timeconsuming simulations and solving the partial differential equations (PDEs) governing the flow field.

Keywords: reduced-order model, wake oscillator, nonlinear, ODEsystem

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

Abstract:

An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.

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Authors: M. H. Kargarnovin, K. Momeni

Abstract:

The study of the stress distribution on a hollow cylindrical fiber placed in a composite material is considered in this work and an analytical solution for this stress distribution has been constructed. Finally some parameters such as fiber-s thickness and fiber-s length are considered and their effects on the distribution of stress have been investigated. For finding the governing relations, continuity equations for the axisymmetric problem in cylindrical coordinate (r,o,z) are considered. Then by assuming some conditions and solving the governing equations and applying the boundary conditions, an equation relates the stress applied to the representative volume element with the stress distribution on the fiber has been found.

Keywords: Axial Loading, Composite, Hollow CylindricalFiber, Stress Distribution.

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Authors: Arunesh Chandra, Pankaj Chandna, Surinder Deswal, Rajesh Kumar Mishra, Rajender Kumar

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The arm length, hand length, hand breadth and middle finger length of 1540 right-handed industrial workers of Haryana state was used to assess the relationship between the upper limb dimensions and stature. Initially, the data were analyzed using basic univariate analysis and independent t-tests; then simple and multiple linear regression models were used to estimate stature using SPSS (version 17). There was a positive correlation between upper limb measurements (hand length, hand breadth, arm length and middle finger length) and stature (p < 0.01), which was highest for hand length. The accuracy of stature prediction ranged from ± 54.897 mm to ± 58.307 mm. The use of multiple regression equations gave better results than simple regression equations. This study provides new forensic standards for stature estimation from the upper limb measurements of male industrial workers of Haryana (India). The results of this research indicate that stature can be determined using hand dimensions with accuracy, when only upper limb is available due to any reasons likewise explosions, train/plane crashes, mutilated bodies, etc. The regression formula derived in this study will be useful for anatomists, archaeologists, anthropologists, design engineers and forensic scientists for fairly prediction of stature using regression equations.

Keywords: Anthropometric dimensions, Forensic identification, Industrial workers, Stature prediction.

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Authors: M. Brahim, I. Bahri, Y. Bernard

Abstract:

Traveling Wave Ultrasonic Motor (TWUM) is a compact, precise, and silent actuator generating high torque at low speed without gears. Moreover, the TWUM has a high holding torque without supply, which makes this motor as an attractive solution for holding position of robotic arms. However, their nonlinear dynamics, and the presence of load-dependent dead zones often limit their use. Those issues can be overcome in closed loop with effective and precise controllers. In this paper, robust H-infinity (H∞) and discrete time RST position controllers are presented. The H∞ controller is designed in continuous time with additional weighting filters to ensure the robustness in the case of uncertain motor model and external disturbances. Robust RST controller based on the pole placement method is also designed and compared to the H∞. Simulink model of TWUM is used to validate the stability and the robustness of the two proposed controllers.

Keywords: Piezoelectric motors, position control, H∞, RST, stability criteria, robustness.

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Authors: Z. Saleh, E. J. Avital, T. Korakianitis

Abstract:

The effect of the blade tip geometry of a high pressure gas turbine is studied experimentally and computationally for high speed leakage flows. For this purpose two simplified models are constructed, one models a flat tip of the blade and the second models a cavity tip of the blade. Experimental results are obtained from a transonic wind tunnel to show the static pressure distribution along the tip wall and provide flow visualization. RANS computations were carried to provide further insight into the mean flow behavior and to calculate the discharge coefficient which is a measure of the flow leaking over the tip. It is shown that in both geometries of tip the flow separates over the tip to form a separation bubble. The bubble is higher for the cavity tip while a complete shock wave system of oblique waves ending with a normal wave can be seen for the flat tip. The discharge coefficient for the flat tip shows less dependence on the pressure ratio over the blade tip than the cavity tip. However, the discharge coefficient for the cavity tip is lower than that of the flat tip, showing a better ability to reduce the leakage flow and thus increase the turbine efficiency.

Keywords: Gas turbine, blade tip leakage flow, transonic flow.

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Authors: Arun Goel

Abstract:

The present paper attempts to investigate the prediction of air entrainment rate and aeration efficiency of a free overfall jets issuing from a triangular sharp crested weir by using regression based modelling. The empirical equations, Support vector machine (polynomial and radial basis function) models and the linear regression techniques were applied on the triangular sharp crested weirs relating the air entrainment rate and the aeration efficiency to the input parameters namely drop height, discharge, and vertex angle. It was observed that there exists a good agreement between the measured values and the values obtained using empirical equations, Support vector machine (Polynomial and rbf) models and the linear regression techniques. The test results demonstrated that the SVM based (Poly & rbf) model also provided acceptable prediction of the measured values with reasonable accuracy along with empirical equations and linear regression techniques in modelling the air entrainment rate and the aeration efficiency of a free overfall jets issuing from triangular sharp crested weir. Further sensitivity analysis has also been performed to study the impact of input parameter on the output in terms of air entrainment rate and aeration efficiency.

Keywords: Air entrainment rate, dissolved oxygen, regression, SVM, weir.

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Authors: Jamal A. Gledan, Othman A. Azzeidani

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During the last decade, Libya established a new Geodetic Datum called Libyan Geodetic Datum 2006 (LGD 2006) by using GPS, whereas the ground traversing method was used to establish the last Libyan datum which was called the Europe Libyan Datum 79 (ELD79). The current research paper introduces ELD79 to LGD2006 coordinate transformation technique, the accurate comparison of transformation between multiple regression equations and the three – parameters model (Bursa-Wolf). The results had been obtained show that the overall accuracy of stepwise multi regression equations is better than that can be determined by using Bursa-Wolf transformation model.

Keywords: Geodetic datum, horizontal control points, traditional similarity transformation model, unconventional transformation techniques.

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Authors: N. Outili, A-H. Meniai

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Modeling transfer phenomena in several chemical engineering operations leads to the resolution of partial differential equations systems. According to the complexity of the operations mechanisms, the equations present a nonlinear form and analytical solution became difficult, we have then to use numerical methods which are based on approximations in order to transform a differential system to an algebraic one.Finite element method is one of numerical methods which can be used to obtain an accurate solution in many complex cases of chemical engineering.The packed columns find a large application like contactor for liquid-liquid systems such solvent extraction. In the literature, the modeling of this type of equipment received less attention in comparison with the plate columns.A mathematical bidimensionnal model with radial and axial dispersion, simulating packed tower extraction behavior was developed and a partial differential equation was solved using the finite element method by adopting the Galerkine model. We developed a Mathcad program, which can be used for a similar equations and concentration profiles are obtained along the column. The influence of radial dispersion was prooved and it can-t be neglected, the results were compared with experimental concentration at the top of the column in the extraction system: acetone/toluene/water.

Keywords: finite element method, Galerkine method, liquidliquid extraction modelling, packed column simulation, two dimensional model

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Authors: Edward J. Kansa, Pavel Holoborodko

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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: Meshless spectrally convergent, partial differential equations, extended arithmetic precision, no branching.

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Authors: Cameron Hamilton, Walter Potter, Gerrit Hoogenboom, Ronald McClendon, Will Hobbs

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A model was constructed to predict the amount of solar radiation that will make contact with the surface of the earth in a given location an hour into the future. This project was supported by the Southern Company to determine at what specific times during a given day of the year solar panels could be relied upon to produce energy in sufficient quantities. Due to their ability as universal function approximators, an artificial neural network was used to estimate the nonlinear pattern of solar radiation, which utilized measurements of weather conditions collected at the Griffin, Georgia weather station as inputs. A number of network configurations and training strategies were utilized, though a multilayer perceptron with a variety of hidden nodes trained with the resilient propagation algorithm consistently yielded the most accurate predictions. In addition, a modeled direct normal irradiance field and adjacent weather station data were used to bolster prediction accuracy. In later trials, the solar radiation field was preprocessed with a discrete wavelet transform with the aim of removing noise from the measurements. The current model provides predictions of solar radiation with a mean square error of 0.0042, though ongoing efforts are being made to further improve the model’s accuracy.

Keywords: Artificial Neural Networks, Resilient Propagation, Solar Radiation, Time Series Forecasting.

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