Search results for: einstein field equations

Authors: Muhammad Sohail Khan, Rehan Ali Shah

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The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method, wire coating die

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of cancer growth under the influence of radiation therapy. The effect of this type of therapy is considered as an additional equation of discussed model. Numerical simulations show that delay, which is added to ordinary differential equations and represent time needed for transformation from one type of cells to the other one, affects the behavior of the system. The validation and verification of proposed model is based on medical data. Analytical results are illustrated by numerical examples of the model dynamics. The model is able to reconstruct dynamics of treatment of cancer and may be used to determine the most effective treatment regimen based on the study of the behavior of individual treatment protocols.

Keywords: mathematical modeling, numerical simulation, ordinary differential equations, radiation therapy

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Authors: H. R. Goshayeshi, M. Khalouei, S. Azarberamman

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This paper presents an experimental investigation regarding the use of Fe2O3 nano particles added to kerosene as a working fluid, under magnetic field. The experiment was made on Oscillating Heat Pipe (OHP). The experiment was performed in order to measure the temperature distribution and compare the heat transfer rate of the oscillating heat pipe with and without magnetic Field. Results showed that the addition of Fe2o3 nano particles under magnetic field improved thermal performance of OHP, compare with non-magnetic field. Furthermore applying a magnetic field enhance the heat transfer characteristic of Fe2O3 in both start up and steady state conditions. This paper presents an experimental investigation regarding the use of Fe2O3 nano particles added to kerosene as a working fluid, under magnetic field. The experiment was made on Oscillating Heat Pipe (OHP). The experiment was performed in order to measure the temperature distribution and compare the heat transfer rate of the oscillating heat pipe with and without magnetic Field. Results showed that the addition of Fe2o3 nano particles under magnetic field improved thermal performance of OHP, compare with non-magnetic field. Furthermore applying a magnetic field enhance the heat transfer characteristic of Fe2O3 in both start up and steady state conditions.

Keywords: experimental, oscillating heat pipe, heat transfer, magnetic field

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Authors: T. S. Soliman, A. G. Galyas, E. V. Rusinova, S. A. Vshivkov

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The liquid crystals combining properties of a liquid and an anisotropic crystal substance play an important role in a science and engineering. Molecules of cellulose and its derivatives have rigid helical conformation, stabilized by intramolecular hydrogen bonds. Therefore the macromolecules of these polymers are capable to be ordered at dissolution and form liquid crystals of cholesteric type. Phase diagrams of solutions of some cellulose derivatives are known. However, little is known about the effect of a magnetic field on the viscosity of polymer solutions. The systems hydroxypropyl cellulose (HPC) – ethanol, HPC – ethylene glycol, HPC–DМАA, HPC–DMF, ethyl cellulose (EC)–ethanol, EC–DMF, were studied in the presence and absence of magnetic field. The solution viscosity was determined on a Rheotest RN 4.1 rheometer. The effect of a magnetic field on the solution properties was studied with the use of two magnets, which induces a magnetic-field-lines directed perpendicularly and parallel to the rotational axis of a rotor. Application of the magnetic field is shown to be accompanied by an increase in the additional assembly of macromolecules, as is evident from a gain in the radii of light scattering particles. In the presence of a magnetic field, the long chains of macromolecules are oriented in parallel with field lines. Such an orientation is associated with the molecular diamagnetic anisotropy of macromolecules. As a result, supramolecular particles are formed, especially in the vicinity of the region of liquid crystalline phase transition. The magnetic field leads to the increase in viscosity of solutions. The results were used to plot the concentration dependence of η/η0, where η and η0 are the viscosities of solutions in the presence and absence of a magnetic field, respectively. In this case, the values of viscosity corresponding to low shear rates were chosen because the concentration dependence of viscosity at low shear rates is typical for anisotropic systems. In the investigated composition range, the values of η/η0 are described by a curve with a maximum.

Keywords: rheology, liquid crystals, magnetic field, cellulose ethers

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Authors: Seung-Yeon Kim

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The Ising model, consisting magnetic spins, is the simplest system showing phase transitions and critical phenomena at finite temperatures. The Ising model has played a central role in our understanding of phase transitions and critical phenomena. Also, the Ising model explains the gas-liquid phase transitions accurately. However, the Ising model in a nonzero magnetic field has been one of the most intriguing and outstanding unsolved problems. We study analytically the partition function zeros in the complex magnetic-field plane and the Yang-Lee edge singularity of the infinite-range Ising model in an external magnetic field. In addition, we compare the Yang-Lee edge singularity of the infinite-range Ising model with that of the square-lattice Ising model in an external magnetic field.

Keywords: Ising ferromagnet, magnetic field, partition function zeros, Yang-Lee edge singularity

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Authors: Naima Benachour, Sabiha Chouchane, J. Paul Chopart

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The objective of this work is to determine the appropriate conditions for a Ni-Zn deposit with good nickel content. The electrodeposition of zinc-nickel on a stainless steel is carried out in a chlorinated bath NiCl2.6H2O, ZnCl2, and H3BO3), whose composition is 1.1 M; 1.8 M; 0.1 M respectively. Studies show the effect of the concentration of NH4Cl, which reveals a significant effect on the reduction and ion transport in the electrolyte. In order to highlight the influence of magnetic field on the chemical composition and morphology of the deposit, chronopotentiometry tests were conducted, the curves obtained inform us that the application of a magnetic field promotes stability of the deposit. Characterization developed deposits was performed by scanning electron microscopy coupled with EDX and specified by the X-ray diffraction.

Keywords: Zn-Ni alloys, electroplating, magnetic field, chronopotentiometry

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Authors: Gebreegziabher Hailu

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This paper presents the development of residual power series methods aimed at efficiently solving stiff differential equations, which pose significant challenges in numerical analysis due to their rapid changes in solution behavior. The RPSM is a numerical approach that generates polynomial-based approximate solutions without the need for linearization, discretization, or perturbation techniques, making it straightforward to implement and less prone to computational errors. We introduce an approach that utilizes power series expansions combined with residual minimization techniques to enhance convergence and stability. By analyzing the theoretical foundations of stiffness, we delve into the formulation of the residual power series method, detailing how it effectively captures the dynamics of stiff systems while maintaining computational efficiency. Numerical experiments demonstrate the method's superiority in terms of accuracy and computational cost when compared to traditional methods like implicit Runge-Kutta or multistep techniques. We also explore adaptive strategies within our framework to automatically adjust parameters based on the stiffness characteristics of the problem at hand. Ultimately, our findings contribute to the broader toolkit for tackling stiff differential equations, offering a robust alternative that promises to streamline computational workflows in various applied mathematics and engineering contexts.

Keywords: residual power series methods, stiff differential equoations, numerical approach, Runge Kutta methods

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma

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Authors: Feng Yang

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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: Ákos Wolf, Richard P. Ray

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Due to the introduction of Eurocode 8, the structural design for seismic and dynamic effects has become more significant in Hungary. This has emphasized the need for more effort to describe the behavior of structures under these conditions. Soil conditions have a significant effect on the response of structures by modifying the stiffness and damping of the soil-structural system and by modifying the seismic action as it reaches the ground surface. Shear modulus (G) and shear wave velocity (v_s), which are often measured in the field, are the fundamental dynamic soil properties for foundation vibration problems, liquefaction potential and earthquake site response analysis. There are several laboratory and in-situ measurement techniques to evaluate dynamic soil properties, but unfortunately, they are often too expensive for general design practice. However, a significant number of correlations have been proposed to determine shear wave velocity or shear modulus from Cone Penetration Tests (CPT), which are used more and more in geotechnical design practice in Hungary. This allows the designer to analyze and compare CPT and seismic test result in order to select the best correlation equations for Hungarian soils and to improve the recommendations for the Hungarian geologic conditions. Based on a literature review, as well as research experience in Hungary, the influence of various parameters on the accuracy of results will be shown. This study can serve as a basis for selecting and modifying correlation equations for Hungarian soils. Test data are taken from seven locations in Hungary with similar geologic conditions. The shear wave velocity values were measured by seismic CPT. Several factors are analyzed including soil type, behavior index, measurement depth, geologic age etc. for their effect on the accuracy of predictions. The final results show an improved prediction method for Hungarian soils

Keywords: CPT correlation, dynamic soil properties, seismic CPT, shear wave velocity

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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: 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

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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: Michael Granado

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The French philosopher Gaston Bachelard’s philosophy of time is articulated in his two works on the subject, the Intuition of the Instant (1932) and his The Dialectic of Duration (1936). Both works present a systematic methodology predicated upon the assumption that our understanding of time has radically changed as a result of Einstein and subsequently needs to be reimagined. Bachelard makes a major distinction in his discussion of time: 1. Time as it is (physical time), 2. Time as we experience it (phenomenological time). This paper will focus on the second distinction, phenomenological time, and explore the connections between Bachelard’s work and contemporary psychology. Several aspects of Bachelard’s philosophy of time nicely complement our current understanding of memory and self and clarify how the self relates to experienced time. Two points, in particular, stand out; the first is the relative nature of subjective time, and the second is the implications of subjective time in the formation of the narrative self. Bachelard introduces two philosophical concepts to explain these points: rhythmanalysis and reverie. By exploring these concepts, it will become apparent that there is an undeniable link between memory, self, and time. Through the use of narrative self, the individual connects and links memories and time together to form a sense of personal identity.

Keywords: Gaston Bachelard, memory, self, time

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Authors: Milad Alizadeh Galdiani, Jabbar Ali Zakeri

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Lateral movement of CWR ballasted track occurs in sharp curves because of the lack of adequate lateral resistance. Several strategies have been proposed and used for increase the lateral resistance of ballasted tracks, but still there are some problems in tracks with small radius curves. In this paper, a new method has been presented for increase the lateral resistance. This method is using the lateral supports as numerical and field studies. In this paper, the field and laboratory tests have been conducted by using the single tie pressure test (STPT) and track panel loading test (LTPT). Then, their results were compared with the numerical results. The results of numerical and field tests showed that the lateral stiffness of ballasted tracks significantly increased when there were lateral supports in ballasted tracks. Also, the track structure had a bilinear behavior.

Keywords: ballasted railway, Lateral resistance, railway buckling, field and numerical studies

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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

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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: M. Kessi

Abstract:

We investigated the effect of the magnetic field on carrier transport phenomena in the transistor channel region of Double-Gate Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET). This explores the Lorentz force and basic physical properties of solids exposed to a constant external magnetic field. The magnetic field modulates the electrons and potential distribution in the case of silicon Tunnel FETs. This modulation shows up in the device's external electrical characteristics such as ON current (ION), subthreshold leakage current (IOF), the threshold voltage (VTH), the magneto-transconductance (gm) and the output magneto-conductance (gDS) of Tunnel FET. Moreover, the channel doping concentration and potential distribution are obtained using the numerical method by solving Poisson’s transport equation in 3D modules semiconductor magnetic sensors available in Silvaco TCAD tools. The numerical simulations of the magnetic nano-sensors are relatively new. In this work, we present the results of numerical simulations based on 3D magnetic sensors. The results show excellent accuracy comportment and good agreement compared with that obtained in the experimental study of MOSFETs technology.

Keywords: single-gate MOSFET, magnetic field, hall field, Lorentz force

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Authors: E. Keramaris, V. Kanakoudis

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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: H. R. Fazlollahi

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Dark Energy origin is unknown and so describing this mysterious component in large scale structure needs to manipulate our theories in general relativity. Although in most models, dark energy arises from extra terms through modifying Einstein-Hilbert action, maybe its origin traces back to fundamental aspects of ground energy of space-time given in quantum mechanics. Hence, diluting space-time in general relativity with quantum mechanics properties leads to the Karolyhazy relation corresponding energy density of quantum fluctuations of space-time. Through generalized uncertainty principle and an eye to Karolyhazy approach in this study we extend energy density of quantum fluctuations of space-time. Also, the application of this idea is considered in late time evolution and we have shown how extra term in generalized uncertainty principle plays as a plausible interaction term role in suggested model.

Keywords: generalized uncertainty principle, karolyhazy approach, agegraphic dark energy, cosmology

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Authors: Davide Gotti, Milan Prodanovic, Sergio Pinilla, David Muñoz-Torrero

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Since its proposal, the Doyle-Fuller-Newman (DFN) lithium-ion battery model has gained popularity in the electrochemical field. In fact, this model provides the user with theoretical support for designing the lithium-ion battery parameters, such as the material particle or the diffusion coefficient adjustment direction. However, the model is mathematically complex as it is composed of several partial differential equations (PDEs) such as Fick’s law of diffusion, the MacInnes and Ohm’s equations, among other phenomena. Thus, to efficiently use the model in a time-domain simulation environment, the selection of the discretization technique is of a pivotal importance. There are several numerical methods available in the literature that can be used to carry out this task. In this study, a comparison between the explicit Euler, Crank-Nicolson, and Chebyshev discretization methods is proposed. These three methods are compared in terms of accuracy, stability, and computational times. Firstly, the explicit Euler discretization technique is analyzed. This method is straightforward to implement and is computationally fast. In this work, the accuracy of the method and its stability properties are shown for the electrolyte diffusion partial differential equation. Subsequently, the Crank-Nicolson method is considered. It represents a combination of the implicit and explicit Euler methods that has the advantage of being of the second order in time and is intrinsically stable, thus overcoming the disadvantages of the simpler Euler explicit method. As shown in the full paper, the Crank-Nicolson method provides accurate results when applied to the DFN model. Its stability does not depend on the integration time step, thus it is feasible for both short- and long-term tests. This last remark is particularly important as this discretization technique would allow the user to implement parameter estimation and optimization techniques such as system or genetic parameter identification methods using this model. Finally, the Chebyshev discretization technique is implemented in the DFN model. This discretization method features swift convergence properties and, as other spectral methods used to solve differential equations, achieves the same accuracy with a smaller number of discretization nodes. However, as shown in the literature, these methods are not suitable for handling sharp gradients, which are common during the first instants of the charge and discharge phases of the battery. The numerical results obtained and presented in this study aim to provide the guidelines on how to select the adequate discretization technique for the DFN model according to the type of application to be performed, highlighting the pros and cons of the three methods. Specifically, the non-eligibility of the simple Euler method for longterm tests will be presented. Afterwards, the Crank-Nicolson and the Chebyshev discretization methods will be compared in terms of accuracy and computational times under a wide range of battery operating scenarios. These include both long-term simulations for aging tests, and short- and mid-term battery charge/discharge cycles, typically relevant in battery applications like grid primary frequency and inertia control and electrical vehicle breaking and acceleration.

Keywords: Doyle-Fuller-Newman battery model, partial differential equations, discretization, numerical methods

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Authors: Dmitry V. Fomichev, Vladimir V. Solonin

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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

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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: Andres Mejia-Ortiz, Catalina Lozada, German R. Santos, Rafael Angulo-Jaramillo, Bernardo Caicedo

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The interaction between atmospheric variables and soil properties is a determining factor when evaluating the flow of water through the soil. This interaction situation directly determines the behavior of the soil and greatly influences the changes that occur in it. The atmospheric variations such as changes in the relative humidity, air temperature, wind velocity and precipitation, are the external variables that reflect a greater incidence in the changes that are generated in the subsoil, as a consequence of the water flow in descending and ascending conditions. These environmental variations have a major importance in the study of the soil because the conditions of humidity and temperature in the soil surface depend on them. In addition, these variations control the thickness of the unsaturated zone and the position of the water table with respect to the surface. However, understanding the relationship between the atmosphere and the soil is a somewhat complex aspect. This is mainly due to the difficulty involved in estimating the changes that occur in the soil from climate changes; since this is a coupled process where act processes of mass transfer and heat. In this research, an experimental field was implemented to study in-situ the interaction between the atmosphere and the soft soils of the city of Bogota, Colombia. The soil under study consists of a 60 cm layer composed of two silts of similar characteristics at the surface and a deep soft clay deposit located under the silky material. It should be noted that the vegetal layer and organic matter were removed to avoid the evapotranspiration phenomenon. Instrumentation was carried on in situ through a field disposal of many measuring devices such as soil moisture sensors, thermocouples, relative humidity sensors, wind velocity sensor, among others; which allow registering the variations of both the atmospheric variables and the properties of the soil. With the information collected through field monitoring, the water balances were made using the Hydrus-1D software to determine the flow conditions that developed in the soil during the study. Also, the moisture profile for different periods and time intervals was determined by the balance supplied by Hydrus 1D; this profile was validated by experimental measurements. As a boundary condition, the actual evaporation rate was included using the semi-empirical equations proposed by different authors. In this study, it was obtained for the rainy periods a descending flow that was governed by the infiltration capacity of the soil. On the other hand, during dry periods. An increase in the actual evaporation of the soil induces an upward flow of water, increasing suction due to the decrease in moisture content. Also, cracks were developed accelerating the evaporation process. This work concerns to the study of soil-atmosphere interaction through the experimental field and it is a very useful tool since it allows considering all the factors and parameters of the soil in its natural state and real values of the different environmental conditions.

Keywords: field monitoring, soil-atmosphere, soft soils, soil-water balance

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Authors: Aigul Manapova

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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: Jesus Ruano, Asensi Oliva

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The hydrodynamic field generated by a jet expansion is computed via three dimensional compressible Large Eddy Simulation (LES). Finite Volume Method (FVM) will be the discretization used during this simulation as well as hybrid schemes based on Kinetic Energy Preserving (KEP) schemes and up-winding Godunov based schemes with instabilities detectors. Velocity and pressure fields will be stored at different surfaces near the jet, but far enough to enclose all the fluctuations, in order to use them as input for the acoustic solver. The acoustic field is obtained in the far-field region at several locations by means of a hybrid method based on Ffowcs-Williams and Hawkings (FWH) equation. This equation will be formulated in the spectral domain, via Fourier Transform of the acoustic sources, which are modeled from the results of the initial simulation. The obtained results will allow the study of the broadband noise generated as well as sound directivities.

Keywords: far-field noise, Ffowcs-Williams and Hawkings, finite volume method, large eddy simulation, jet noise

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Authors: Radoslaw Pytlak, Damian Suski

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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: Hyun-Ho Lee, Kee-Won Kim

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The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes. Finite field arithmetic includes addition, multiplication, division and inversion operations. Addition is very simple and can be implemented with an extremely simple circuit. The other operations are much more complex. The multiplication is the most important for cryptosystems, such as the elliptic curve cryptosystem, since computing exponentiation, division, and computing multiplicative inverse can be performed by computing multiplication iteratively. In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis. Also, based on the multiplication algorithm, we present an efficient semi-systolic multiplier over finite field. The multiplier has less space and time complexities compared to related multipliers. As compared to the corresponding existing structures, the multiplier saves at least 5% area, 50% time, and 53% area-time (AT) complexity. Accordingly, it is well suited for VLSI implementation and can be easily applied as a basic component for computing complex operations over finite field, such as inversion and division operation.

Keywords: finite field, Montgomery multiplication, systolic array, cryptography

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Authors: Najafi S., Heidai R., Jamei R., Tofigh F.

Abstract:

In order to study the effects of magnetic field on the root system and growth of Phaseolus vulgaris, an experiment was conducted in 2012. The possible involvement of magnetic field (MF) pretreatment in physiological factors of Phaseolus vulgaris was investigated. Seeds were subjected to 10 days with 1.8 mT of magnetic field for 1h per day. MF pretreatment decreased the plant height, fresh and dry weight, length of root and length of shoot, Chlorophyll a, Chlorophyll b and carotenoid in 10 days old seedling. In addition, activity of enzymes such as Catalase and Guaiacol peroxidase was decreased due to MF exposure. Also, the total Protein and DPPH content of the treated by magnetic field was not significantly changed in compare to control groups, while the flavonoid, Phenol and prolin content of the treated of the treated by magnetic field was significantly changed in compare to control groups. Lateral branches of roots and secondary roots increased with MF. The results suggest that pretreatment of this MF plays important roles in changes in crop productivity. In all cases there was observed a slight stimulating effect of the factors examined. The growth dynamics were weakened. The plants were shorter. Moreover, the effect of a magnetic field on the crop of Phaseolus vulgaris and its structure was small.

Keywords: carotenoid, Chlorophyll a, Chlorophyll b, DPPH, enzymes, flavonoid, germination, growth, phenol, proline, protein, magnetic field, phaseolus vulgaris

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