Search results for: dispersive wave equations

Authors: Benoit Rougier, Alexandre Lefrancois, Herve Aubert

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Microwave interrogation in the range 10-100 GHz is identified as an advanced technique to investigate simultaneously shock and particle velocity measurements. However, it requires the understanding of electromagnetic wave propagation in a multi-layered moving media. The existing models limit their approach to wave guides or evaluate the velocities with a fitting method, restricting therefore the domain of validity and the precision of the results. Moreover, few data of permittivity on high explosives at these frequencies under dynamic compression have been reported. In this paper, shock and particle velocities are computed concurrently for steady and unsteady shocks for various inert and reactive materials, via a propagation model based on Doppler shifts and signal amplitude. Refractive index of the material under compression is also calculated. From experimental data processing, it is demonstrated that Hugoniot curve can be evaluated. The comparison with published results proves the accuracy of the proposed method. This microwave interrogation technique seems promising for shock and detonation waves studies.

Keywords: electromagnetic propagation, experimental setup, Hugoniot measurement, shock propagation

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Authors: M. Saadi, S. E. H. Abaidia, M. Y. Mokeddem.

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We present the results of a systematic and comparative study of the bulk, the structural properties, and phonon calculations of aluminum alloys using several exchange–correlations functional theory (DFT) with different plane-wave basis pseudo potential techniques. Density functional theory implemented by the Vienna Ab Initio Simulation Package (VASP) technique is applied to calculate the bulk and the structural properties of several structures. The calculations were performed for within several exchange–correlation functional and pseudo pententials available in this code (local density approximation (LDA), generalized gradient approximation (GGA), projector augmented wave (PAW)). The lattice dynamic code “PHON” developed by Dario Alfè was used to calculate some thermodynamics properties and phonon dispersion relation frequency distribution of Aluminium alloys using the VASP LDA PAW and GGA PAW results. The bulk and structural properties of the calculated structures were compared to different experimental and calculated works.

Keywords: DFT, exchange-correlation functional, LDA, GGA, pseudopotential, PAW, VASP, PHON, phonon dispersion

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Authors: Arnab Majumdar, Srimani Sen

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In this paper, a vivid simulated study has been made on 35 GHz Ka-band window frequency in order to judge and compare the DC and high frequency properties of cubic ZnB-GaN with the existing hexagonal 4H-SiC. A flat profile p⁺pnn⁺ DDR structure of impatt is chosen and is optimized at a particular bias current density with respect to efficiency and output power taking into consideration the effect of mobile space charge also. The simulated results obtained reveals the strong potentiality of impatts based on both cubic ZnB-GaN and hexagonal 4H-SiC. The DC-to-millimeter wave conversion efficiency for cubic ZnB-GaN impatt obtained is 50% with an estimated output power of 2.83 W at an optimized bias current density of 2.5×10⁸ A/m². The conversion efficiency and estimated output power in case of hexagonal 4H-SiC impatt obtained is 22.34% and 40 W respectively at an optimum bias current density of 0.06×10⁸ A/m².

Keywords: cubic ZnB-GaN, hexagonal 4H-SiC, double drift impatt diode, millimetre wave, optimised bias current density, wide band gap semiconductor

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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: 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: 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

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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: S. Mohammadzamani, B. Kordi

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Wireless electric field sensors are in high demand in the number of applications that requires measuring electric field such as investigations of high power systems and testing the high voltage apparatus. Passive wireless electric field sensors are most desired since they do not require a source of power and are interrogated wirelessly. A passive wireless electric field sensor has been designed and fabricated by our research group. In the wireless interrogation system of the sensor, a wireless radio frequency impulse generator needs to be employed. A compact wireless impulse generator composed of an integrated resonant switched oscillator (SWO) and a pulse-radiating antenna has been designed and fabricated in this research. The fundamental of Switched Oscillators was introduced by C.E.Baum. A Switched Oscillator consists of a low impedance transmission line charged by a DC source, through large impedance at desired frequencies and terminated to a high impedance antenna at one end and a fast closing switch at the other end. Once the line is charged, the switch will close and short-circuit the transmission line. Therefore, a fast transient wave will be generated and travels along the transmission line. Because of the mismatch between the antenna and the transmission line, only a part of fast transient wave will be radiated, and a portion of the fast-transient wave will reflect back. At the other end of the transmission line, there is a closed switch. Consequently, a second reflection with a reversed sign will propagate towards the antenna and the wave continues back and forth. hence, at the terminal of the antenna, there will be a series of positive and negative pulses with descending amplitude. In this research a single ended quarter wavelength Switched Oscillator has been designed and simulated at 800MHz. The simulation results show that the designed Switched Oscillator generates pulses with decreasing amplitude at the frequency of 800MHz with the maximum amplitude of 10V and bandwidth of about 10MHz at the antenna end. The switched oscillator has been fabricated using a 6cm long coaxial cable transmission line which is charged by a DC source and an 8cm monopole antenna as the pulse radiating antenna. A 90V gas discharge switch has been employed as the fast closing switch. The Switched oscillator sends a series of pulses with decreasing amplitude at the frequency of 790MHz with the maximum amplitude of 0.3V in the distance of 30 cm.

Keywords: electric field measurement, impulse radiating antenna, switched oscillator, wireless impulse generator

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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: 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: Sergey Kozlov, Juliya Kozlova

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Introduction: The increased attention of researchers to an explosive trauma around the world is associated with a constant renewal of military weapons and a significant increase in terrorist activities using explosive devices. Explosive wave is a well known damaging factor of explosion. The most sensitive to the action of explosive wave in the human body are the head brain, lungs, intestines, urine bladder. The severity of damage to these organs depends on the distance from the explosion epicenter to the object, the power of the explosion, presence of barriers, parameters of the body position, and the presence of protective clothing. One of the places where a shock wave acts, in human tissues and organs, is the vascular endothelial barrier, which suffers the greatest damage in the head brain and lungs. The objective of the study was to determine the pathomorphological changes of the head brain followed the action of explosive wave. Materials and methods of research: To achieve the purpose of the study, there have been studied 6 male corpses delivered to the morgue of Municipal Institution "Dnipropetrovsk regional forensic bureau" during 2014-2016 years. The cause of death of those killed was a military explosive injury. After a visual external assessment of the head brain, for histological study there was conducted the 1 x 1 x 1 cm/piece sampling from different parts of the head brain, i.e. the frontal, parietal, temporal, occipital sites, and also from the cerebellum, pons, medulla oblongata, thalamus, walls of the lateral ventricles, the bottom of the 4th ventricle. Pieces of the head brain were immersed in 10% formalin solution for 24 hours. After fixing, the paraffin blocks were made from the material using the standard method. Then, using a microtome, there were made sections of 4-6 micron thickness from paraffin blocks which then were stained with hematoxylin and eosin. Microscopic analysis was performed using a light microscope with x4, x10, x40 lenses. Results of the study: According to the results of our study, injuries of the head brain were divided into macroscopic and microscopic. Macroscopic injuries were marked according to the results of visual assessment of haemorrhages under the membranes and into the substance, their nature, and localisation, areas of softening. In the microscopic study, our attention was drawn to both vascular changes and those of neurons and glial cells. Microscopic qualitative analysis of histological sections of different parts of the head brain revealed a number of structural changes both at the cellular and tissue levels. Typical changes in most of the studied areas of the head brain included damages of the vascular system. The most characteristic microscopic sign was the separation of vascular walls from neuroglia with the formation of perivascular space. Along with this sign, wall fragmentation of these vessels, haemolysis of erythrocytes, formation of haemorrhages in the newly formed perivascular spaces were found. In addition to damages of the cerebrovascular system, destruction of the neurons, presence of oedema of the brain tissue were observed in the histological sections of the brain. On some sections, the head brain had a heterogeneous step-like or wave-like nature. Conclusions: The pathomorphological microscopic changes in the brain, identified in the study on the died of explosive traumas, can be used for diagnostic purposes in conjunction with other characteristic signs of explosive trauma in forensic and pathological studies. The complex of microscopic signs in the head brain, i.e. separation of blood vessel walls from neuroglia with the perivascular space formation, fragmentation of walls of these blood vessels, erythrocyte haemolysis, formation of haemorrhages in the newly formed perivascular spaces is the direct indication of explosive wave action.

Keywords: blast wave, neurotrauma, human, brain

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Authors: Fortaki Tarek, S. Bedra

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In this paper, the effects of both uniaxial anisotropy in the substrate and high Tc superconducting patch on the resonant frequency, half-power bandwidth, and radiation patterns are investigated using an electric field integral equation and the spectral domain Green’s function. The analysis has been based on a full electromagnetic wave model with London’s equations and the Gorter-Casimir two-fluid model has been improved to investigate the resonant and radiation characteristics of high Tc superconducting rectangular microstrip patch in the case where the patch is printed on electric-magnetic uniaxially anisotropic substrate materials. The stationary phase technique has been used for computing the radiation electric field. The obtained results demonstrate a considerable improvement in the half-power bandwidth, of the rectangular microstrip patch, by using a superconductor patch instead of a perfect conductor one. Further results show that high Tc superconducting rectangular microstrip patch on the uniaxial substrate with properly selected electric and magnetic anisotropy ratios is more advantageous than the one on the isotropic substrate by exhibiting wider bandwidth and radiation characteristic. This behavior agrees with that discovered experimentally for superconducting patches on isotropic substrates. The calculated results have been compared with measured one available in the literature and excellent agreement has been found.

Keywords: high Tc superconducting microstrip patch, electric-magnetic anisotropic substrate, Galerkin method, surface complex impedance with boundary conditions, radiation patterns

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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: Alono Thorie, Ananya Mukhopadhyay

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Ooid bearing horizons of the Proterozoic Kunihar Formation, Simla Group, Lesser Himalaya have been addressed in the present work. The study is concentrated around the outskirts of Arki town, Solan district, Himachal Pradesh, India. Based on the sedimentary facies associations, the processes that promote the formation of ooids have been documented. The facies associations that have been recorded are: (i) Oolitic-Intraclastic grainstone (FA1), (ii) Oolitic grainstone (FA2), (iii) Boundstone (FA3), (iv) Dolomudstone (FA4) and (v) Rudstone (FA5). Oolitic-Intraclastic grainstone (FA1) mainly consists of well sorted ooids with concentric laminae and intraclasts. Large ooids with grain sizes more than 4 mm are characteristic of oolites throughout the area. Normally graded beds consisting of ooids and intraclasts are frequently documented in storm sediments in shelf environments and carbonate platforms. The well-sorted grainstone fabric indicates deposition in a high-energy shoal with tidal currents and storm reworking. FA2 comprises spherical to elliptical grains up to 8.5cm in size with concentric cortex and micritic nuclei. Peloids in FA2 are elliptical, rounded objects <0.3 mm in size. FA1 and FA2 have been recorded alongside boundstones (FA3) comprising stromatolites having columnar, wavy and domal morphology. Boundstones (FA3) reflect microbial growth in carbonate platforms and reefs. Dolomudstones (FA4) interbedded with cross laminated sandstones and erosional surfaces reflect sedimentation in storm dominated zones below fair-weather wave base. Rudstone (FA5) is composed of oolitic grainstone (FA2), boundstone (FA3) and dolomudstone (FA4). These clasts are few mm to more than 10 cm in length. Rudstones indicate deposition along a slope with intermittent influence of wave currents and storm activities. Most ooids from the Kunihar Formation are regular ooids with abundance of broken ooids. Compound and concentric ooids indicating medium to low energy environments are present but scarce. Ooids from high energy domains are more dominant than ooids developed from low energy environments. The unusually large size of the Kunihar ooids (more than 8.5 cm) is rare in the geological record. Development of carbonate deposits such as oolitic- intraclastic Grainstones (FA1), oolitic grainstones (FA2) and rudstones (FA5), and reflect deposition in an agitated beach environment with abundant microbial activity and high energy shallow marine waters influenced by tide, wave and storm currents. Occurrences of boundstone (FA4) or stromatolitic carbonate amongst oolitic facies (FA1 and FA2) and appearance of compound and concentric ooids indicate intervals of calm in between agitated phases of storm, wave and tidal activities.

Keywords: proterozoic, Simla Group, ooids, stromatolites

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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: Ahmad H. Abdelgwad, Ahmed A. Nashat

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Landmine detection is an important and yet challenging problem remains to be solved. Ground Penetrating Radar (GPR) is a powerful and rapidly maturing technology for subsurface threat identification. The detection methodology of GPR depends mainly on the contrast of the dielectric properties of the searched target and its surrounding soil. This contrast produces a partial reflection of the electromagnetic pulses that are being transmitted into the soil and then being collected by the GPR.  One of the most critical hardware components for the performance of GPR is the antenna system. The current paper explores the design and simulation of a pyramidal horn antenna operating at L-band frequencies (1- 2 GHz) to detect a landmine. A prototype model of the GPR system setup is developed to simulate full wave analysis of the electromagnetic fields in different soil types. The contrast in the dielectric permittivity of the landmine and the sandy soil is the most important parameter to be considered for detecting the presence of landmine. L-band horn antenna is proved to be well-versed in the investigation of landmine detection.

Keywords: full wave analysis, ground penetrating radar, horn antenna design, landmine detection

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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: Jaime E. Munoz, Jose C. Arcos, Oscar E. Bautista, Ivan E. Campos

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The influence of slippage phenomenon over the destabilization and atomization mechanisms induced via surface acoustic waves on a Newtonian, millimeter-sized, drop deposited on a hydrophilic substrate is studied theoretically. By implementing the Navier-slip model and a lubrication-type approach into the equations which govern the dynamic response of a drop exposed to acoustic stress, a highly nonlinear evolution equation for the air-liquid interface is derived in terms of the acoustic capillary number and the slip coefficient. By numerically solving such an evolution equation, the Spatio-temporal deformation of the drop's free surface is obtained; in this context, atomization of the initial drop into micron-sized droplets is predicted at our numerical model once the acoustically-driven capillary waves reach a critical value: the instability length. Our results show slippage phenomenon at systems with partial and complete wetting favors the formation of capillary waves at the free surface, which traduces in a major volume of liquid being atomized in comparison to the no-slip case for a given time interval. In consequence, slippage at the wall possesses the capability to affect and improve the atomization rate for a drop exposed to a high-frequency acoustic field.

Keywords: capillary instability, lubrication theory, navier-slip condition, SAW atomization

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Authors: M. G. Ghanem, A. M. M. A. Allam, Diaa E. Fawzy, Mehmet Faruk Cengiz

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This paper is devoted to the design and implementation of a smartwatch textile antenna for Wi-Fi bio-medical applications in millimetric wave bands. The antenna is implemented on a leather textile-based substrate to be embedded in a smartwatch. It enables the watch to pick Wi-Fi signals without the need to be connected to a mobile through Bluetooth. It operates at 60 GHz or WiGig (Wireless Gigabit Alliance) band with a wide band for higher rate applications. It also could be implemented over many stratified layers of the body organisms to be used in the diagnosis of many diseases like diabetes and cancer. The structure is designed and simulated using CST (Studio Suite) program. The wearable patch antenna has an octagon shape, and it is implemented on leather material that acts as a flexible substrate with a size of 5.632 x 6.4 x 2 mm3, a relative permittivity of 2.95, and a loss tangent of 0.006. The feeding is carried out using differential feed (discrete port in CST). The work provides five antenna implementations; antenna without ground, a ground is added at the back of the antenna in order to increase the antenna gain, the substrate dimensions are increased to 15 x 30 mm2 to resemble the real hand watch size, layers of skin and fat are added under the ground of the antenna to study the effect of human body tissues human on the antenna performance. Finally, the whole structure is bent. It is found that the antenna can achieve a simulated peak realized gain in dB of 5.68, 7.28, 6.15, 3.03, and 4.37 for antenna without ground, antenna with the ground, antenna with larger substrate dimensions, antenna with skin and fat, and bent structure, respectively. The antenna with ground exhibits high gain; while adding the human organisms absorption, the gain is degraded because of human absorption. The bent structure contributes to higher gain.

Keywords: bio medical engineering, millimetric wave, smart watch, textile antennas, Wi-Fi

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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: 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: Shyh Ming Chern

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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: Abdulatif Abdusalam, Mohamed Shaban

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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: David Alejandro Lazo-Vasquez, Jorge Luis Balino

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In the petroleum industry, multiphase flow occurs when oil, gas, and water are transported in the same pipe through large pipeline systems. The flow can take different patterns depending on parameters like fluid velocities, pipe diameter, pipe inclination, and fluid properties. Mainly, intermittent flow is produced by the natural propagation of short and long waves, according to the Kelvin-Helmholtz Stability Theory. To model stratified flow and the onset of intermittent flow, it is crucial to have knowledge of short and long waves behavior. The two-fluid model, frequently employed for characterizing multiphase systems, becomes ill-posed for high liquid and gas velocities and large inclination angles, for short waves can develop infinite growth rates. We are interested in focusing attention on long-wave instability, which leads to the production of roll waves that may grow and result in the transition from stratified flow to intermittent flow. In this study, global and local linear stability analyses for dynamic and kinematic stability criteria predict the regions of stability of the flow for different pipe inclinations and fluid velocities in regularized and non-regularized systems, concurrently. It was possible to distinguish when: wave growth rates are absolutely bounded (stable stratified smooth flow), waves have finite growth rates (unstable stratified wavy flow), and when the equation system becomes elliptic and hyperbolization is needed. In order to bound short wave growth rates and regularize the equation system, we incorporated some lower and higher-order terms like interfacial drag and surface tension, respectively.

Keywords: linear stability analysis, multiphase flow, onset of slugging, two-fluid model regularization

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

Abstract:

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: K. Farheen, A. Munir

Abstract:

Seismic response of the multi-storey buildings is created by the interaction of both the structure and underlying soil medium. The seismic design philosophy is incorporated using response modification factor 'R'. Current code based values of 'R' factor does not reflect the SSI problem as it is based on fixed base condition. In this study, the modified values of 'R' factor for moment resisting frame (MRF) considering SSI are evaluated. The response of structure with and without SSI has been compared using equivalent linear static and nonlinear static pushover analyses for 10-storied moment resisting frame building. The building is located in seismic zone 2B situated on different soils with shear wave velocity (Vₛ) of 300m/sec (SD) and 1200m/s (SB). Code based 'R' factor value for building frame system has been taken as 5.5. Soil medium is modelled using identical but mutually independent horizontal and vertical springs. It was found that the modified 'R' factor values have been decreased by 47% and 43% for soil SD and SB respectively as compared to that of code based 'R' factor.

Keywords: buildings, SSI, shear wave velocity, R factor

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

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

Procedia PDF Downloads 363

Authors: B. M. Moda, L. F. Secco

Abstract:

Through free and fair elections and others less democratic processes, Latin America has been gradually turning into a right-wing political region. In order to understand these recent changes, this paper aims to discuss the origin and the traits of the pink wave in the subcontinent, the reasons for its current rollback and future projections for left-wing in the region. The methodology used in this paper will be descriptive and analytical combined with secondary sources mainly from the social and political sciences fields. The canons of the Washington Consensus was implemented by the majority of the Latin American governments in the 80s and 90s under the social democratic and right-wing parties. The neoliberal agenda caused political, social and economic dissatisfaction bursting into a new political configuration for the region. It started in 1998 when Hugo Chávez took the office in Venezuela through the Fifth Republic Movement under the socialist flag. From there on, Latin America was swiped by the so-called ‘pink wave’, term adopted to define the rising of self-designated left-wing or center-left parties with a progressive agenda. After Venezuela, countries like Chile, Brazil, Argentina, Uruguay, Bolivia, Equator, Nicaragua, Paraguay, El Salvador and Peru got into the pink wave. The success of these governments was due a post-neoliberal agenda focused on cash transfers programs, increasing of public spending, and the straightening of national market. The discontinuation of the preference for the left-wing started in 2012 with the coup against Fernando Lugo in Paraguay. In 2015, the chavismo in Venezuela lost the majority of the legislative seats. In 2016, an impeachment removed the Brazilian president Dilma Rousself from office who was replaced by the center-right vice-president Michel Temer. In the same year, Mauricio Macri representing the right-wing party Proposta Republicana was elected in Argentina. In 2016 center-right and liberal, Pedro Pablo Kuczynski was elected in Peru. In 2017, Sebastián Piñera was elected in Chile through the center-right party Renovación Nacional. The pink wave current rollback points towards some findings that can be arranged in two fields. Economically, the 2008 financial crisis affected the majority of the Latin American countries and the left-wing economic policies along with the end of the raw materials boom and the subsequent shrinking of economic performance opened a flank for popular dissatisfaction. In Venezuela, the 2014 oil crisis reduced the revenues for the State in more than 50% dropping social spending, creating an inflationary spiral, and consequently loss of popular support. Politically, the death of Hugo Chavez in 2013 weakened the ‘socialism of the twenty first century’ ideal, which was followed by the death of Fidel Castro, the last bastion of communism in the subcontinent. In addition, several cases of corruption revealed during the pink wave governments made the traditional politics unpopular. These issues challenge the left-wing to develop a future agenda based on innovation of its economic program, improve its legal and political compliance practices, and to regroup its electoral forces amid the social movements that supported its ascension back in the early 2000s.

Keywords: Latin America, political parties, left-wing, right-wing, pink wave

Procedia PDF Downloads 240