Search results for: first order ordinary differential equations

Authors: Bahatti̇n Ki̇mençe, Uğur Ki̇mençe

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In this study, the purpose of obtaining the influence functions of the displacement discontinuity in an anisotropic elastic medium is to produce the boundary element equations. A Displacement Discontinuous Method formulation (DDM) is presented with the aim of modeling two-dimensional elastic fracture problems. This formulation is found by analytical integration of the fundamental solution along a straight-line crack. With this purpose, Kelvin's fundamental solutions for anisotropic media on an infinite plane are used to form dipoles from singular loads, and the various combinations of the said dipoles are used to obtain the influence functions of displacement discontinuity. This study introduces a technique for coupling Fictitious Stress Method (FSM) and DDM; the reason for applying this technique to some examples is to demonstrate the effectiveness of the proposed coupling method. In this study, displacement discontinuity equations are obtained by using dipole solutions calculated with known singular force solutions in an anisotropic medium. The displacement discontinuities method obtained from the solutions of these equations and the fictitious stress methods is combined and compared with various examples. In this study, one or more crack problems with various geometries in rectangular plates in finite and infinite regions, under the effect of tensile stress with coupled FSM and DDM in the anisotropic environment, were examined, and the effectiveness of the coupled method was demonstrated. Since crack problems can be modeled more easily with DDM, it has been observed that the use of DDM has increased recently. In obtaining the displacement discontinuity equations, Papkovitch functions were used in Crouch, and harmonic functions were chosen to satisfy various boundary conditions. A comparison is made between two indirect boundary element formulations, DDM, and an extension of FSM, for solving problems involving cracks. Several numerical examples are presented, and the outcomes are contrasted to existing analytical or reference outs.

Keywords: displacement discontinuity method, fictitious stress method, crack problems, anisotropic material

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Authors: Nurul Bin Ibrahim

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Advancements in neural networks have offered valuable insights into Fluid Dynamics, notably in addressing turbulence-related challenges. In this research, we introduce multiple applications of models of neural networks, namely Feed-Forward and Recurrent Neural Networks, to explore the relationship between jet formations and stratified turbulence within stochastically excited Boussinesq systems. Using machine learning tools like TensorFlow and PyTorch, the study has created models that effectively mimic and show the underlying features of the complex patterns of jet formation and stratified turbulence. These models do more than just help us understand these patterns; they also offer a faster way to solve problems in stochastic systems, improving upon traditional numerical techniques to solve stochastic differential equations such as the Euler-Maruyama method. In addition, the research includes a thorough comparison with the Statistical State Dynamics (SSD) approach, which is a well-established method for studying chaotic systems. This comparison helps evaluate how well neural networks can help us understand the complex relationship between jet formations and stratified turbulence. The results of this study underscore the potential of neural networks in computational physics and fluid dynamics, opening up new possibilities for more efficient and accurate simulations in these fields.

Keywords: neural networks, machine learning, computational fluid dynamics, stochastic systems, simulation, stratified turbulence

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Authors: Lei Zhang, Jean-Michel Ghidaglia, Anela Kumbaro

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This work focuses on numerical simulation of two-phase flows based on the bi-fluid six-equation model widely used in many industrial areas, such as nuclear power plant safety analysis. A pressure-based numerical method is adopted in our studies due to the fact that in two-phase flows, it is common to have a large range of Mach numbers because of the mixture of liquid and gas, and density-based solvers experience stiffness problems as well as a loss of accuracy when approaching the low Mach number limit. This work extends the semi-implicit pressure solver in the nuclear component CUPID code, where the governing equations are solved on unstructured grids with co-located variables to accommodate complicated geometries. A conservative version of the solver is developed in order to capture exactly the shock in one-phase flows, and is extended to two-phase situations. An inter-facial pressure term is added to the bi-fluid model to make the system hyperbolic and to establish a well-posed mathematical problem that will allow us to obtain convergent solutions with refined meshes. The ability of the numerical method to treat phase appearance and disappearance as well as the behavior of the scheme at low Mach numbers will be demonstrated through several numerical results. Finally, inter-facial mass and heat transfer models are included to deal with situations when mass and energy transfer between phases is important, and associated industrial numerical benchmarks with tabulated EOS (equations of state) for fluids are performed.

Keywords: two-phase flows, numerical simulation, bi-fluid model, unstructured grids, phase appearance and disappearance

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Authors: Sabrina Tabassum

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Using Census Data for Housing and Population of Australia 2001, 2006, 2011, and 2016, this paper shows the existence of wage differences between natives and immigrants in Australia. Addressing the heterogeneous nature of immigrants, this study group the immigrants in three broad categories- migrants from English speaking countries and migrants from India and China. Migrants from English speaking countries and India earn more than the natives per week, whereas migrants from China earn far less than the natives per week. Oaxaca decomposition suggests that major part of this differential is unexplained. Using the occupational segregation concept and Brown decomposition, this study indicates that migrants from India and China would have been earned more than the natives if they had the same occupation distribution as natives due to their individual characteristics. Within occupation, wage differences are more prominent than inter-occupation wage differences for immigrants from China and India.

Keywords: Australia, labour, migration, wage

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Authors: Soheil Arash Moghadam, Abdol R. Kashani Nia, Ali Akrami Zade

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Considering numerous applications of Autonomous Underwater Vehicles in various industries, there has been plenty of researches and studies on the motion control of such vehicles. One of the useful aspects for studying is the guidance of these vehicles. In this paper, while presenting motion equations with six degrees of freedom for Autonomous Underwater Vehicles, Proportional Navigation Guidance Law and the first order sliding mode control for TAIPAN AUV was used to address its guidance for the purpose of collision with a moving target.

Keywords: Autonomous Underwater Vehicle (AUV), degree of freedom (DOF), hydrodynamic, line of sight(LOS), proportional navigation guidance(PNG), sliding mode control(SMC)

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Authors: Aurora Cerri, Niko Pullojani

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Long-term differential settlement between the bridge structure and the bridge embankment typically results in an abrupt grade change, causing driver discomfort, impairing driver safety, and exerting a potentially excessive impact traffic loading on the abutment. This paper has analysed a case of study showing the effect of an approaching slab realized in a bridge constructed at Tirane-Elbasan Motorway. The layer thickness under the slab is modeled as homogenous, the slab is a reinforced concrete structure and over that the asphaltic layers take place. Analysis indicates that reinforced concrete approaching slab distributes the stresses quite uniformly into the road fill layers and settlements varies in a range less than 2.50 cm in the total slab length of 6.00 m with a maximum slope of 1/240. Results taken from analytical analysis are compared with topographic measurements done on field and they carry great similarities.

Keywords: approach slab, bridge, road pavement, differential settlement

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: Larry V. Aceres, Jesryl B. Paulite, Emelie M. Pelicano, J. A. Esteban, Mamangun

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Citrus rind borer still the most important pest infesting pummelo in the Philippines particularly in the Davao region. Hence, management of the pest is very important for successful pummelo production. This study was conducted to assess the effectiveness of the different control strategies against citrus rind borer; to determine the best treatment in controlling citrus rind borer; and to calculate the profitability of the various treatments in pummelo production. The experiment was laid-out in Completely Randomized Design (CRD) with five treatments replicated three times. The treatments were: T1- curry tree leaf leachate, T2- neem tree leaf leachate, T3- bagging with an ordinary net, T4- treated check (chlorpyrifos & betacyflutrin) and T5- untreated check. Data were analyzed using the Analysis of Variance and the differences among treatment means were computed using the Tukey’s Honest Significant Difference. The results of the study revealed that the curry tree leaf leachate and bagging treatments provide significant protection to the pummelo fruits which is comparable with the treated check (chlorpyrifos & betacyflutrin). Neem tree leaf leachate is not effective in controlling citrus rind borer which is comparable with the untreated check. In cost and return analysis, the most economical and effective is the bagging treatment using ordinary net.

Keywords: curry tree, neem tree, bagging, citrus rind borer

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Authors: Teodrose Atnafu Abegaze, P. K. Sharma

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In this study, an attempt has been made to study the behavior of breakthrough curves in both layered and mixed heterogeneous soil by conducting experiments in long soil columns. Sodium chloride has been used as a conservative tracer in the experiment. Advective dispersive transport equations, including equilibrium sorption and first-order degradation coefficients, are used for solute transport through mobile-immobile porous media. In order to do the governing equation for solute transport, there are explicit and implicit schemes for our condition; we use an implicit scheme to numerically model the solute concentration. Results of experimental breakthrough curves indicate that the behavior of observed breakthrough curves is approximately similar in both cases of layered and mixed soil, while earlier arrival of solute concentration is obtained in the case of mixed soil. It means that the types of heterogeneity of the soil media affect the behavior of solute concentration. Finally, it is also shown that the asymptotic dispersion model simulates the experimental data better than the constant and linear distance-dependent dispersion models.

Keywords: numerical method, distance dependant dispersion, reactive transport, experiment

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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: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

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

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

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Authors: Mahtab Delfan Azari, Ali Noorzad, Ahmadreza Mahboubi Ardakani

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Municipal solid waste landfills have relatively high temperature which is caused by anaerobic and aerobic degradation. The temperature that is produced is almost 40-70°C. Since this temperature will remain for many years, considering it for studying landfill behavior and its soil is so important. By considering the temperature of landfill, the obtained results will become more logical and more realistic. Vertical displacement and differential settlement are two important values which are studied here. Differential displacements could expand cracks in liner and cover. If cracks appear in the liner, the leachate and gases will propagate to media and hence should be noticed carefully. The present research is focused on the thermo-hydro-mechanical modeling of landfill with finite element method. First, the heat transfer of the landfill is modeled and the temperature is estimated. Then, the results of thermo-hydro-mechanical results are presented to investigate landfill behavior more accurately.

Keywords: finite element method, heat transfer, landfill behavior, thermo-hydro-mechanical modeling

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Authors: Yi Zhang, Yuan Tian, Jiehua Chen, Sihong Gu

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Chip-scale spin-exchange relaxation free (SERF) atomic magnetometer makes use of millimeter-scale vapor cells micro-fabricated by Micro-electromechanical Systems (MEMS) technique and SERF mechanism, resulting in the characteristics of high spatial resolution and high sensitivity. It is useful for biomagnetic imaging including magnetoencephalography and magnetocardiography. In a prevailing scheme, circularly polarized on-resonance laser beam is adapted for both pumping and probing the atomic polarization. And the magnetic-field-sensitive signal is extracted by transmission laser intensity enhancement as a result of atomic polarization increase on zero field level crossing resonance. The scheme is very suitable for integration, however, the laser amplitude modulation (AM) noise and laser frequency modulation to amplitude modulation (FM-AM) noise is superimposed on the photon shot noise reducing the signal to noise ratio (SNR). To suppress AM and FM-AM noise the paper puts forward a novel scheme which adopts circularly polarized on-resonance light pumping and linearly polarized frequency-detuning laser probing. The transmission beam is divided into transmission and reflection beams by a polarization analyzer, the angle between the analyzer's transmission polarization axis and frequency-detuning laser polarization direction is set to 45°. The magnetic-field-sensitive signal is extracted by polarization rotation enhancement of frequency-detuning laser which induces two beams intensity difference increase as the atomic polarization increases. Therefore, AM and FM-AM noise in two beams are common-mode and can be almost entirely canceled by differential detection. We have carried out an experiment to study our scheme. The experiment reveals that the noise in the differential signal is obviously smaller than that in each beam. The scheme is promising to be applied for developing more sensitive chip-scale magnetometer.

Keywords: atomic magnetometer, chip scale, differential detection, spin-exchange relaxation free

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Authors: Anne Schattel, Mitja Echim, Christof Büskens

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Trajectory planning for deep space missions has become a recent topic of great interest. Flying to space objects like asteroids provides two main challenges. One is to find rare earth elements, the other to gain scientific knowledge of the origin of the world. Due to the enormous spatial distances such explorer missions have to be performed unmanned and autonomously. The mathematical field of optimization and optimal control can be used to realize autonomous missions while protecting recourses and making them safer. The resulting algorithms may be applied to other, earth-bound applications like e.g. deep sea navigation and autonomous driving as well. The project KaNaRiA ('Kognitionsbasierte, autonome Navigation am Beispiel des Ressourcenabbaus im All') investigates the possibilities of cognitive autonomous navigation on the example of an asteroid mining mission, including the cruise phase and approach as well as the asteroid rendezvous, landing and surface exploration. To verify and test all methods an interactive, real-time capable simulation using virtual reality is developed under KaNaRiA. This paper focuses on the specific challenge of the guidance during the cruise phase of the spacecraft, i.e. trajectory optimization and optimal control, including first solutions and results. In principle there exist two ways to solve optimal control problems (OCPs), the so called indirect and direct methods. The indirect methods are being studied since several decades and their usage needs advanced skills regarding optimal control theory. The main idea of direct approaches, also known as transcription techniques, is to transform the infinite-dimensional OCP into a finite-dimensional non-linear optimization problem (NLP) via discretization of states and controls. These direct methods are applied in this paper. The resulting high dimensional NLP with constraints can be solved efficiently by special NLP methods, e.g. sequential quadratic programming (SQP) or interior point methods (IP). The movement of the spacecraft due to gravitational influences of the sun and other planets, as well as the thrust commands, is described through ordinary differential equations (ODEs). The competitive mission aims like short flight times and low energy consumption are considered by using a multi-criteria objective function. The resulting non-linear high-dimensional optimization problems are solved by using the software package WORHP ('We Optimize Really Huge Problems'), a software routine combining SQP at an outer level and IP to solve underlying quadratic subproblems. An application-adapted model of impulsive thrusting, as well as a model of an electrically powered spacecraft propulsion system, is introduced. Different priorities and possibilities of a space mission regarding energy cost and flight time duration are investigated by choosing different weighting factors for the multi-criteria objective function. Varying mission trajectories are analyzed and compared, both aiming at different destination asteroids and using different propulsion systems. For the transcription, the robust method of full discretization is used. The results strengthen the need for trajectory optimization as a foundation for autonomous decision making during deep space missions. Simultaneously they show the enormous increase in possibilities for flight maneuvers by being able to consider different and opposite mission objectives.

Keywords: deep space navigation, guidance, multi-objective, non-linear optimization, optimal control, trajectory planning.

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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: Derrouazin Mohammed Redhouane, Souakri Mohammed Lotfi, Henini Ghania

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This work consists, first of all, of mastering one of the powerful process simulation tools currently used in the industrial processes, which is the HYSYS sizing software, and second, of simulating a petroleum distillation column. This study is divided into two parts; where the first one consists of a dimensioning of the column with a fast approximating method using state equations, iterative calculations, and then a precise simulation method with the HYSYS software. The second part of this study is a hydrodynamic study in order to verify by obtained results the proper functioning of the plates.

Keywords: industry process engineering, water distillation, environment, HYSYS simulation tool

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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: Ofosuhene O. Apenteng, Noor Azina Ismail

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Over the last several years, concern has developed over how to minimize the spread of HIV/AIDS epidemic in many countries. AIDS epidemic has tremendously stimulated the development of mathematical models of infectious diseases. The transmission dynamics of HIV infection that eventually developed AIDS has taken a pivotal role of much on building mathematical models. From the initial HIV and AIDS models introduced in the 80s, various improvements have been taken into account as how to model HIV/AIDS frameworks. In this paper, we present the impact of migration on the spread of HIV/AIDS. Epidemic model is considered by a system of nonlinear differential equations to supplement the statistical method approach. The model is calibrated using HIV incidence data from Malaysia between 1986 and 2011. Bayesian inference based on Markov Chain Monte Carlo is used to validate the model by fitting it to the data and to estimate the unknown parameters for the model. The results suggest that the migrants stay for a long time contributes to the spread of HIV. The model also indicates that susceptible individual becomes infected and moved to HIV compartment at a rate that is more significant than the removal rate from HIV compartment to AIDS compartment. The disease-free steady state is unstable since the basic reproduction number is 1.627309. This is a big concern and not a good indicator from the public heath point of view since the aim is to stabilize the epidemic at the disease equilibrium.

Keywords: epidemic model, HIV, MCMC, parameter estimation

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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: 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: 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: Utsav Bhardwaj, Shyama Prasad Das

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To meet the extensive requirements of thermal management of the circuit card assemblies (CCAs), satellites, PCBs, microprocessors, any other electronic circuitry, pulsating heat pipes (PHPs) have emerged in the recent past as one of the best solutions technically. But industrial application of PHPs is still unexplored up to a large extent due to their poor reliability. There are several systems as well as operational parameters which not only affect the performance of an operating PHP, but also decide whether the PHP can operate sustainably or not. Functioning may completely be halted for some particular combinations of the values of system and operational parameters. Among the system parameters, adiabatic length is one of the important ones. In the present work, a simplest single branch PHP system with an adiabatic section has been considered. It is assumed to have only one vapour bubble and one liquid plug. First, the system has been mathematically modeled using film evaporation/condensation model, followed by the steps of recognition of equilibrium zone, non-dimensionalization and linearization. Then proceeding with a periodical solution of the linearized and reduced differential equations, stability analysis has been performed. Slow and fast variables have been identified, and averaging approach has been used for the slow ones. Ultimately, temporal evolution of the PHP is predicted by numerically solving the averaged equations, to know whether the oscillations are likely to sustain/decay temporally. Stability threshold has also been determined in terms of some non-dimensional numbers formed by different groupings of system and operational parameters. A combined analytical and numerical approach has been used, and it has been found that for each combination of all other parameters, there exists a maximum length of the adiabatic section beyond which the PHP cannot function at all. This length has been called as “Critical Adiabatic Length (L_ac)”. For adiabatic lengths greater than “L_ac”, oscillations are found to be always decaying sooner or later. Dependence of “L_ac” on some other parameters has also been checked and correlated at certain evaporator & condenser section temperatures. “L_ac” has been found to be linearly increasing with increase in evaporator section length (L_e), whereas the condenser section length (L_c) has been found to have almost no effect on it upto a certain limit. But at considerably large condenser section lengths, “L_ac” is expected to decrease with increase in “L_c” due to increased wall friction. Rise in static pressure (p_r) exerted by the working fluid reservoir makes “L_ac” rise exponentially whereas it increases cubically with increase in the inner diameter (d) of PHP. Physics of all such variations has been given a good insight too. Thus, a methodology for quantification of the critical adiabatic length for any possible set of all other parameters of PHP has been established.

Keywords: critical adiabatic length, evaporation/condensation, pulsating heat pipe (PHP), thermal management

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Shabnam Pashaei, Mohammadali Badamchizadeh

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This paper presents a new fractional-order terminal sliding mode control for synchronization of two different fractional-order chaotic systems with uncertainty and external disturbances. A fractional-order integral type nonlinear switching surface is presented. Then, using the Lyapunov stability theory and sliding mode theory, a fractional-order control law is designed to synchronize two different fractional-order chaotic systems. Finally, a simulation example is presented to illustrate the performance and applicability of the proposed method. Based on numerical results, the proposed controller ensures that the states of the controlled fractional-order chaotic response system are asymptotically synchronized with the states of the drive system.

Keywords: terminal sliding mode control, fractional-order calculus, chaotic systems, synchronization

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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: Marek Dlapa

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The algebraic approach is applied to the control of the HiMAT (Highly Maneuverable Aircraft Technology). The objective is to find a robust controller which guarantees robust stability and decoupled control of longitudinal model of a scaled remotely controlled vehicle version of the advanced fighter HiMAT. Control design is performed by decoupling the nominal MIMO (multi-input multi-output) system into two identical SISO (single-input single-output) plants which are approximated by a 4th order transfer function. The algebraic approach is then used for pole placement design, and the nominal closed-loop poles are tuned so that the peak of the µ-function is minimal. As an optimization tool, evolutionary algorithm Differential Migration is used in order to overcome the multimodality of the cost function yielding simple controller with decoupling for nominal plant which is compared with the D-K iteration through simulations of standard longitudinal manoeuvres documenting decoupled control obtained from algebraic approach for nominal plant as well as worst case perturbation.

Keywords: algebraic approach, evolutionary computation, genetic algorithms, HiMAT, robust control, structured singular value

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Authors: Yasser Rammah, Wolf-Christian Mueller

Abstract:

Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: D. Pradeep Mitra, Prafulla

Abstract:

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

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

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Authors: Ali Benali Djouher Leila

Abstract:

Labiovelarization of velar consonants and labials is a very widespread phenomenon. It is attested in all the major northern Berber dialects. Only the Tuareg is totally unaware of it. But, even within the large Berber-speaking regions of the north, it is very unstable: it may be completely absent in certain dialects (such as the Bougie region in Kabylie), and its extension and frequency can vary appreciably between the dialects which know it. Some dialects of Great Kabylia or the Chleuh domain, for example, "labiovélarize" more than others from the same region. Thus, in Great Kabylia, the adjective "large" will be pronounced: amqqwran with the At Yiraten and amqqran with the At Yanni, a few kilometers away. One of the problems with them is deciding whether it is one or two phonemes. All the criteria used by linguists in this kind of case lead to the conclusion that they are unique phonemes (a phoneme and not a succession of two phonemes, / k + w /, for example). The phonetic and phonological criteria are moreover clearly confirmed by the morphological data since, in the system of verbal alternations, these complex segments are treated as single phonemes: agree, "to draw, to fetch water," akwer, "to fly," have exactly the same morphology as as "jealous," arem" taste," Ames, "dirty" or afeg, "steal" ... verbs with two radical consonants (type aCC). At the level of notation, both scientific and usual, it is, therefore, necessary to represent the labiovélarized by a single letter, possibly accompanied by a diacritic. In fact, actual practices are diverse. - The scientific representation of type does not seem adequate for current use because its realization is easy only on a microcomputer. The Berber Documentation File used a small ° (of n °) above the writing line: k °, g ° ... which has the advantage of being easy to achieve since it is part of general typographical conventions in Latin script and that it is present on a typewriter keyboard. Mouloud Mammeri, then the Berber Study Group of Vincennes (Tisuraf review), and a majority of Kabyle practitioners over the last twenty years have used the succession "consonant +" semi-vowel / w / "(CW) on the same line of writing; for all the reasons explained previously, this practice is not a good solution and should be abandoned, especially as it particularizes Kabyle in the Berber ensemble. In this study, we were interested in two velar consonants, / g / and / k /, labiovellarized: / gw / and the / kw / (we adopted the addition of the "w") for the representation for ease of writing in graphical mode. It is a question of trying to characterize these four consonants in order to see if they have different places of articulation and if they are distinct (if these velars are distinct from their labiovellarized counterpart). This characterization is done using locus equations.

Keywords: berber consonants;, labiovelarization, locus equations, acoustical caracterization, kabylian dialect, algerian language

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