Search results for: algebra and equations
1213 Characterization of the Near-Wake of an Ahmed Body Profile
Authors: Stéphanie Pellerin, Bérengére Podvin, Luc Pastur
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In aerovehicles context, the flow around an Ahmed body profile is simulated using the velocity-vorticity formulation of the Navier-Stokes equations, associated to a penalization method for solids and Large Eddy Simulation for turbulence. The study focuses both on the ground influence on the flow and on the dissymetry of the wake, observed for a ground clearance greater than 10% of the body height H. Unsteady and mean flows are presented and analyzed. POD study completes the analysis and gives information on the most energetic structures of the flow.Keywords: Ahmed body, bi-stability, LES, near wake
Procedia PDF Downloads 6021212 Parallel Multisplitting Methods for Differential Systems
Authors: Malika El Kyal, Ahmed Machmoum
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We prove the superlinear convergence of asynchronous multi-splitting methods applied to differential equations. This study is based on the technique of nested sets. It permits to specify kind of the convergence in the asynchronous mode.The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.Keywords: parallel methods, asynchronous mode, multisplitting, ODE
Procedia PDF Downloads 5161211 Tsunami Wave Height and Flow Velocity Calculations Based on Density Measurements of Boulders: Case Studies from Anegada and Pakarang Cape
Authors: Zakiul Fuady, Michaela Spiske
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Inundation events, such as storms and tsunamis can leave onshore sedimentary evidence like sand deposits or large boulders. These deposits store indirect information on the related inundation parameters (e.g., flow velocity, flow depth, wave height). One tool to reveal these parameters are inverse models that use the physical characteristics of the deposits to refer to the magnitude of inundation. This study used boulders of the 2004 Indian Ocean Tsunami from Thailand (Pakarang Cape) and form a historical tsunami event that inundated the outer British Virgin Islands (Anegada). For the largest boulder found in Pakarang Cape with a volume of 26.48 m³ the required tsunami wave height is 0.44 m and storm wave height are 1.75 m (for a bulk density of 1.74 g/cm³. In Pakarang Cape the highest tsunami wave height is 0.45 m and storm wave height are 1.8 m for transporting a 20.07 m³ boulder. On Anegada, the largest boulder with a diameter of 2.7 m is the asingle coral head (species Diploria sp.) with a bulk density of 1.61 g/cm³, and requires a minimum tsunami wave height of 0.31 m and storm wave height of 1.25 m. The highest required tsunami wave height on Anegada is 2.12 m for a boulder with a bulk density of 2.46 g/cm³ (volume 0.0819 m³) and the highest storm wave height is 5.48 m (volume 0.216 m³) from the same bulk density and the coral type is limestone. Generally, the higher the bulk density, volume, and weight of the boulders, the higher the minimum tsunami and storm wave heights required to initiate transport. It requires 4.05 m/s flow velocity by Nott’s equation (2003) and 3.57 m/s by Nandasena et al. (2011) to transport the largest boulder in Pakarang Cape, whereas on Anegada, it requires 3.41 m/s to transport a boulder with diameter 2.7 m for both equations. Thus, boulder equations need to be handled with caution because they make many assumptions and simplifications. Second, the physical boulder parameters, such as density and volume need to be determined carefully to minimize any errors.Keywords: tsunami wave height, storm wave height, flow velocity, boulders, Anegada, Pakarang Cape
Procedia PDF Downloads 2281210 Fully Coupled Porous Media Model
Authors: Nia Mair Fry, Matthew Profit, Chenfeng Li
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This work focuses on the development and implementation of a fully implicit-implicit, coupled mechanical deformation and porous flow, finite element software tool. The fully implicit software accurately predicts classical fundamental analytical solutions such as the Terzaghi consolidation problem. Furthermore, it can capture other analytical solutions less well known in the literature, such as Gibson’s sedimentation rate problem and Coussy’s problems investigating wellbore stability for poroelastic rocks. The mechanical volume strains are transferred to the porous flow governing equation in an implicit framework. This will overcome some of the many current industrial issues, which use explicit solvers for the mechanical governing equations and only implicit solvers on the porous flow side. This can potentially lead to instability and non-convergence issues in the coupled system, plus giving results with an accountable degree of error. The specification of a fully monolithic implicit-implicit coupled porous media code sees the solution of both seepage-mechanical equations in one matrix system, under a unified time-stepping scheme, which makes the problem definition much easier. When using an explicit solver, additional input such as the damping coefficient and mass scaling factor is required, which are circumvented with a fully implicit solution. Further, improved accuracy is achieved as the solution is not dependent on predictor-corrector methods for the pore fluid pressure solution, but at the potential cost of reduced stability. In testing of this fully monolithic porous media code, there is the comparison of the fully implicit coupled scheme against an existing staggered explicit-implicit coupled scheme solution across a range of geotechnical problems. These cases include 1) Biot coefficient calculation, 2) consolidation theory with Terzaghi analytical solution, 3) sedimentation theory with Gibson analytical solution, and 4) Coussy well-bore poroelastic analytical solutions.Keywords: coupled, implicit, monolithic, porous media
Procedia PDF Downloads 1301209 Characteristics of Middle Grade Students' Solution Strategies While Reasoning the Correctness of the Statements Related to Numbers
Authors: Ayşegül Çabuk, Mine Işıksal
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Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.Keywords: reasoning, mathematics learning, middle grade students
Procedia PDF Downloads 4151208 The Development of a New Block Method for Solving Stiff ODEs
Authors: Khairil I. Othman, Mahfuzah Mahayaddin, Zarina Bibi Ibrahim
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We develop and demonstrate a computationally efficient numerical technique to solve first order stiff differential equations. This technique is based on block method whereby three approximate points are calculated. The Cholistani of varied step sizes are presented in divided difference form. Stability regions of the formulae are briefly discussed in this paper. Numerical results show that this block method perform very well compared to existing methods.Keywords: block method, divided difference, stiff, computational
Procedia PDF Downloads 4151207 Modal Approach for Decoupling Damage Cost Dependencies in Building Stories
Authors: Haj Najafi Leila, Tehranizadeh Mohsen
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Dependencies between diverse factors involved in probabilistic seismic loss evaluation are recognized to be an imperative issue in acquiring accurate loss estimates. Dependencies among component damage costs could be taken into account considering two partial distinct states of independent or perfectly-dependent for component damage states; however, in our best knowledge, there is no available procedure to take account of loss dependencies in story level. This paper attempts to present a method called "modal cost superposition method" for decoupling story damage costs subjected to earthquake ground motions dealt with closed form differential equations between damage cost and engineering demand parameters which should be solved in complex system considering all stories' cost equations by the means of the introduced "substituted matrixes of mass and stiffness". Costs are treated as probabilistic variables with definite statistic factors of median and standard deviation amounts and a presumed probability distribution. To supplement the proposed procedure and also to display straightforwardness of its application, one benchmark study has been conducted. Acceptable compatibility has been proven for the estimated damage costs evaluated by the new proposed modal and also frequently used stochastic approaches for entire building; however, in story level, insufficiency of employing modification factor for incorporating occurrence probability dependencies between stories has been revealed due to discrepant amounts of dependency between damage costs of different stories. Also, more dependency contribution in occurrence probability of loss could be concluded regarding more compatibility of loss results in higher stories than the lower ones, whereas reduction in incorporation portion of cost modes provides acceptable level of accuracy and gets away from time consuming calculations including some limited number of cost modes in high mode situation.Keywords: dependency, story-cost, cost modes, engineering demand parameter
Procedia PDF Downloads 1701206 Analysis of the Occurrence of Hydraulic Fracture Phenomena in Roudbar Lorestan Dam
Authors: Masoud Ghaemi, MohammadJafar Hedayati, Faezeh Yousefzadeh, Hoseinali Heydarzadeh
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According to the statistics of the International Committee on Large Dams, internal erosion and piping (scour) are major causes of the destruction of earth-fill dams. If such dams are constructed in narrow valleys, the valley walls will increase the arching of the dam body due to the transfer of vertical and horizontal stresses, so the occurrence of hydraulic fracturing in these embankments is more likely. Roudbar Dam in Lorestan is a clay-core pebble earth-fill dam constructed in a relatively narrow valley in western Iran. Three years after the onset of impoundment, there has been a fall in dam behavior. Evaluation of the dam behavior based on the data recorded on the instruments installed inside the dam body and foundation confirms the occurrence of internal erosion in the lower and adjacent parts of the core on the left support (abutment). The phenomenon of hydraulic fracturing is one of the main causes of the onset of internal erosion in this dam. Accordingly, the main objective of this paper is to evaluate the validity of this hypothesis. To evaluate the validity of this hypothesis, the dam behavior during construction and impoundment has been first simulated with a three-dimensional numerical model. Then, using validated empirical equations, the safety factor of the occurrence of hydraulic fracturing phenomenon upstream of the dam score was calculated. Then, using the artificial neural network, the failure time of the given section was predicted based on the maximum stress trend created. The study results show that steep slopes of valley walls, sudden changes in coefficient, and differences in compressibility properties of dam body materials have caused considerable stress transfer from core to adjacent valley walls, especially at its lower levels. This has resulted in the coefficient of confidence of the occurrence of hydraulic fracturing in each of these areas being close to one in each of the empirical equations used.Keywords: arching, artificial neural network, FLAC3D, hydraulic fracturing, internal erosion, pore water pressure
Procedia PDF Downloads 1711205 Islam and Globalization: Accommodation or Containment of One by the Other
Authors: Mohammed Isah Shehu
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This paper examined the context of globalization and Islam and accommodation or containment of one by the other. The paper is born out of the misconception and misunderstanding among many people that globalization is purely Western, anti-Islam and that Islam, globalization and Islam are diametrically opposed as such have no places for accommodating each other. The study used secondary sources to gather data. The study found that from its origin, Islam is in the whole context, a globalized religion and the contemporary globalization is already contained by Islam; that while contemporary globalization is centered on Western world, values and preferences (Western civilization, information and communication technology, free markets, trade and investments); some of the major foundation works that are aiding globalization were originally handiworks of past great Muslims (Islamic civilizations, Order of Algebra, tools of Navigation, Calligraphy, Medicine, Astronomy et cetera) whose major values are not Islamic; with globalization the Muslims have greater opportunities of spreading of Islam and practicing it in a most conducive atmosphere, easy and fast linkage with their fellow Muslim brothers wherever they may be; easier and freer world of trade and have the best opportunities to most things. The study however observed that Western contemporary globalization poses threats to religions such as those of globalization of immorality, injustice, trade with anti-Islamic terms and conditions, internationalized crime et cetera. Muslims would have to avoid or be cautious of many things for Islam is a complete religion that has what is forbidden and allowed (halaal and haramm) based on principles of (Shariah, justice to all, humanity and compassion, obedience to and seeking Allah’s pleasure); to Muslims, Contemporary globalization has to be in conformity with original provisions of Islam. The study recommended that Muslims must rise up in seeking knowledge on Islam and all other fields, further intellectual explorations of works by Muslim scholars/thinkers so that any advancement in globalization would be properly domesticated within Islam for the Muslims to make optimum use of any advancement to the benefit of Islam.Keywords: accommodation, containment, Islam, globalization
Procedia PDF Downloads 2781204 Modification of Newton Method in Two Points Block Differentiation Formula
Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim
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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.Keywords: modified Newton, stiff, BBDF, Jacobian matrix
Procedia PDF Downloads 3651203 Analytical Technique for Definition of Internal Forces in Links of Robotic Systems and Mechanisms with Statically Indeterminate and Determinate Structures Taking into Account the Distributed Dynamical Loads and Concentrated Forces
Authors: Saltanat Zhilkibayeva, Muratulla Utenov, Nurzhan Utenov
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The distributed inertia forces of complex nature appear in links of rod mechanisms within the motion process. Such loads raise a number of problems, as the problems of destruction caused by a large force of inertia; elastic deformation of the mechanism can be considerable, that can bring the mechanism out of action. In this work, a new analytical approach for the definition of internal forces in links of robotic systems and mechanisms with statically indeterminate and determinate structures taking into account the distributed inertial and concentrated forces is proposed. The relations between the intensity of distributed inertia forces and link weight with geometrical, physical and kinematic characteristics are determined in this work. The distribution laws of inertia forces and dead weight make it possible at each position of links to deduce the laws of distribution of internal forces along the axis of the link, in which loads are found at any point of the link. The approximation matrixes of forces of an element under the action of distributed inertia loads with the trapezoidal intensity are defined. The obtained approximation matrixes establish the dependence between the force vector in any cross-section of the element and the force vector in calculated cross-sections, as well as allow defining the physical characteristics of the element, i.e., compliance matrix of discrete elements. Hence, the compliance matrixes of an element under the action of distributed inertial loads of trapezoidal shape along the axis of the element are determined. The internal loads of each continual link are unambiguously determined by a set of internal loads in its separate cross-sections and by the approximation matrixes. Therefore, the task is reduced to the calculation of internal forces in a final number of cross-sections of elements. Consequently, it leads to a discrete model of elastic calculation of links of rod mechanisms. The discrete model of the elements of mechanisms and robotic systems and their discrete model as a whole are constructed. The dynamic equilibrium equations for the discrete model of the elements are also received in this work as well as the equilibrium equations of the pin and rigid joints expressed through required parameters of internal forces. Obtained systems of dynamic equilibrium equations are sufficient for the definition of internal forces in links of mechanisms, which structure is statically definable. For determination of internal forces of statically indeterminate mechanisms (in the way of determination of internal forces), it is necessary to build a compliance matrix for the entire discrete model of the rod mechanism, that is reached in this work. As a result by means of developed technique the programs in the MAPLE18 system are made and animations of the motion of the fourth class mechanisms of statically determinate and statically indeterminate structures with construction on links the intensity of cross and axial distributed inertial loads, the bending moments, cross and axial forces, depending on kinematic characteristics of links are obtained.Keywords: distributed inertial forces, internal forces, statically determinate mechanisms, statically indeterminate mechanisms
Procedia PDF Downloads 2121202 Numerical Modelling of Hydrodynamic Drag and Supercavitation Parameters for Supercavitating Torpedoes
Authors: Sezer Kefeli, Sertaç Arslan
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In this paper, supercavitationphenomena, and parameters are explained, and hydrodynamic design approaches are investigated for supercavitating torpedoes. In addition, drag force calculation methods ofsupercavitatingvehicles are obtained. Basically, conventional heavyweight torpedoes reach up to ~50 knots by classic hydrodynamic techniques, on the other hand super cavitating torpedoes may reach up to ~200 knots, theoretically. However, in order to reachhigh speeds, hydrodynamic viscous forces have to be reduced or eliminated completely. This necessity is revived the supercavitation phenomena that is implemented to conventional torpedoes. Supercavitation is a type of cavitation, after all, it is more stable and continuous than other cavitation types. The general principle of supercavitation is to separate the underwater vehicle from water phase by surrounding the vehicle with cavitation bubbles. This situation allows the torpedo to operate at high speeds through the water being fully developed cavitation. Conventional torpedoes are entitled as supercavitating torpedoes when the torpedo moves in a cavity envelope due to cavitator in the nose section and solid fuel rocket engine in the rear section. There are two types of supercavitation phase, these are natural and artificial cavitation phases. In this study, natural cavitation is investigated on the disk cavitators based on numerical methods. Once the supercavitation characteristics and drag reduction of natural cavitationare studied on CFD platform, results are verified with the empirical equations. As supercavitation parameters cavitation number (), pressure distribution along axial axes, drag coefficient (C_?) and drag force (D), cavity wall velocity (U_?) and dimensionless cavity shape parameters, which are cavity length (L_?/d_?), cavity diameter(d_ₘ/d_?) and cavity fineness ratio (〖L_?/d〗_ₘ) are investigated and compared with empirical results. This paper has the characteristics of feasibility study to carry out numerical solutions of the supercavitation phenomena comparing with empirical equations.Keywords: CFD, cavity envelope, high speed underwater vehicles, supercavitating flows, supercavitation, drag reduction, supercavitation parameters
Procedia PDF Downloads 1601201 Evolutional Substitution Cipher on Chaotic Attractor
Authors: Adda Ali-Pacha, Naima Hadj-Said
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Nowadays, the security of information is primarily founded on the calculation of algorithms that confidentiality depend on the number of bits necessary to define a cryptographic key. In this work, we introduce a new chaotic cryptosystem that we call evolutional substitution cipher on a chaotic attractor. In this research paper, we take the Henon attractor. The evolutional substitution cipher on Henon attractor is based on the principle of monoalphabetic cipher and it associates the plaintext at a succession of real numbers calculated from the attractor equations.Keywords: cryptography, substitution cipher, chaos theory, Henon attractor, evolutional substitution cipher
Procedia PDF Downloads 4181200 Modelling and Simulation of Aero-Elastic Vibrations Using System Dynamic Approach
Authors: Cosmas Pandit Pagwiwoko, Ammar Khaled Abdelaziz Abdelsamia
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Flutter as a phenomenon of flow-induced and self-excited vibration has to be recognized considering its harmful effect on the structure especially in a stage of aircraft design. This phenomenon is also important for a wind energy harvester based on the fluttering surface due to its effective operational velocity range. This multi-physics occurrence can be presented by two governing equations in both fluid and structure simultaneously in respecting certain boundary conditions on the surface of the body. In this work, the equations are resolved separately by two distinct solvers, one-time step of each domain. The modelling and simulation of this flow-structure interaction in ANSYS show the effectiveness of this loosely coupled method in representing flutter phenomenon however the process is time-consuming for design purposes. Therefore, another technique using the same weak coupled aero-structure is proposed by using system dynamics approach. In this technique, the aerodynamic forces were calculated using singularity function for a range of frequencies and certain natural mode shapes are transformed into time domain by employing an approximation model of fraction rational function in Laplace variable. The representation of structure in a multi-degree-of-freedom coupled with a transfer function of aerodynamic forces can then be simulated in time domain on a block-diagram platform such as Simulink MATLAB. The dynamic response of flutter at certain velocity can be evaluated with another established flutter calculation in frequency domain k-method. In this method, a parameter of artificial structural damping is inserted in the equation of motion to assure the energy balance of flow and vibrating structure. The simulation in time domain is particularly interested as it enables to apply the structural non-linear factors accurately. Experimental tests on a fluttering airfoil in the wind tunnel are also conducted to validate the method.Keywords: flutter, flow-induced vibration, flow-structure interaction, non-linear structure
Procedia PDF Downloads 3021199 Deriving Generic Transformation Matrices for Multi-Axis Milling Machine
Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin
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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.Keywords: CAM, multi-axis milling machining, transformation matrix, rotation angles
Procedia PDF Downloads 4691198 Electromagnetic Simulation Based on Drift and Diffusion Currents for Real-Time Systems
Authors: Alexander Norbach
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The script in this paper describes the use of advanced simulation environment using electronic systems (Microcontroller, Operational Amplifiers, and FPGA). The simulation may be used for all dynamic systems with the diffusion and the ionisation behaviour also. By additionally required observer structure, the system works with parallel real-time simulation based on diffusion model and the state-space representation for other dynamics. The proposed deposited model may be used for electrodynamic effects, including ionising effects and eddy current distribution also. With the script and proposed method, it is possible to calculate the spatial distribution of the electromagnetic fields in real-time. For further purpose, the spatial temperature distribution may be used also. With upon system, the uncertainties, unknown initial states and disturbances may be determined. This provides the estimation of the more precise system states for the required system, and additionally, the estimation of the ionising disturbances that occur due to radiation effects. The results have shown that a system can be also developed and adopted specifically for space systems with the real-time calculation of the radiation effects only. Electronic systems can take damage caused by impacts with charged particle flux in space or radiation environment. In order to be able to react to these processes, it must be calculated within a shorter time that ionising radiation and dose is present. All available sensors shall be used to observe the spatial distributions. By measured value of size and known location of the sensors, the entire distribution can be calculated retroactively or more accurately. With the formation, the type of ionisation and the direct effect to the systems and thus possible prevent processes can be activated up to the shutdown. The results show possibilities to perform more qualitative and faster simulations independent of kind of systems space-systems and radiation environment also. The paper gives additionally an overview of the diffusion effects and their mechanisms. For the modelling and derivation of equations, the extended current equation is used. The size K represents the proposed charge density drifting vector. The extended diffusion equation was derived and shows the quantising character and has similar law like the Klein-Gordon equation. These kinds of PDE's (Partial Differential Equations) are analytically solvable by giving initial distribution conditions (Cauchy problem) and boundary conditions (Dirichlet boundary condition). For a simpler structure, a transfer function for B- and E- fields was analytically calculated. With known discretised responses g₁(k·Ts) and g₂(k·Ts), the electric current or voltage may be calculated using a convolution; g₁ is the direct function and g₂ is a recursive function. The analytical results are good enough for calculation of fields with diffusion effects. Within the scope of this work, a proposed model of the consideration of the electromagnetic diffusion effects of arbitrary current 'waveforms' has been developed. The advantage of the proposed calculation of diffusion is the real-time capability, which is not really possible with the FEM programs available today. It makes sense in the further course of research to use these methods and to investigate them thoroughly.Keywords: advanced observer, electrodynamics, systems, diffusion, partial differential equations, solver
Procedia PDF Downloads 1231197 A Mathematical Model for Studying Landing Dynamics of a Typical Lunar Soft Lander
Authors: Johns Paul, Santhosh J. Nalluveettil, P. Purushothaman, M. Premdas
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Lunar landing is one of the most critical phases of lunar mission. The lander is provided with a soft landing system to prevent structural damage of lunar module by absorbing the landing shock and also assure stability during landing. Presently available software are not capable to simulate the rigid body dynamics coupled with contact simulation and elastic/plastic deformation analysis. Hence a separate mathematical model has been generated for studying the dynamics of a typical lunar soft lander. Parameters used in the analysis includes lunar surface slope, coefficient of friction, initial touchdown velocity (vertical and horizontal), mass and moment of inertia of lander, crushing force due to energy absorbing material in the legs, number of legs and geometry of lander. The mathematical model is capable to simulate plastic and elastic deformation of honey comb, frictional force between landing leg and lunar soil, surface contact simulation, lunar gravitational force, rigid body dynamics and linkage dynamics of inverted tripod landing gear. The non linear differential equations generated for studying the dynamics of lunar lander is solved by numerical method. Matlab programme has been used as a computer tool for solving the numerical equations. The position of each kinematic joint is defined by mathematical equations for the generation of equation of motion. All hinged locations are defined by position vectors with respect to body fixed coordinate. The vehicle rigid body rotations and motions about body coordinate are only due to the external forces and moments arise from footpad reaction force due to impact, footpad frictional force and weight of vehicle. All these force are mathematically simulated for the generation of equation of motion. The validation of mathematical model is done by two different phases. First phase is the validation of plastic deformation of crushable elements by employing conservation of energy principle. The second phase is the validation of rigid body dynamics of model by simulating a lander model in ADAMS software after replacing the crushable elements to elastic spring element. Simulation of plastic deformation along with rigid body dynamics and contact force cannot be modeled in ADAMS. Hence plastic element of primary strut is replaced with a spring element and analysis is carried out in ADAMS software. The same analysis is also carried out using the mathematical model where the simulation of honeycomb crushing is replaced by elastic spring deformation and compared the results with ADAMS analysis. The rotational motion of linkages and 6 degree of freedom motion of lunar Lander about its CG can be validated by ADAMS software by replacing crushing element to spring element. The model is also validated by the drop test results of 4 leg lunar lander. This paper presents the details of mathematical model generated and its validation.Keywords: honeycomb, landing leg tripod, lunar lander, primary link, secondary link
Procedia PDF Downloads 3371196 Soliton Solutions in (3+1)-Dimensions
Authors: Magdy G. Asaad
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Solitons are among the most beneficial solutions for science and technology for their applicability in physical applications including plasma, energy transport along protein molecules, wave transport along poly-acetylene molecules, ocean waves, constructing optical communication systems, transmission of information through optical fibers and Josephson junctions. In this talk, we will apply the bilinear technique to generate a class of soliton solutions to the (3+1)-dimensional nonlinear soliton equation of Jimbo-Miwa type. Examples of the resulting soliton solutions are computed and a few solutions are plotted.Keywords: Pfaffian solutions, N-soliton solutions, soliton equations, Jimbo-Miwa
Procedia PDF Downloads 4411195 Chebyshev Polynomials Relad with Fibonacci and Lucas Polynomials
Authors: Vandana N. Purav
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Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials. Procedia PDF Downloads 3581194 Detection of Flood Prone Areas Using Multi Criteria Evaluation, Geographical Information Systems and Fuzzy Logic. The Ardas Basin Case
Authors: Vasileiou Apostolos, Theodosiou Chrysa, Tsitroulis Ioannis, Maris Fotios
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The severity of extreme phenomena is due to their ability to cause severe damage in a small amount of time. It has been observed that floods affect the greatest number of people and induce the biggest damage when compared to the total of annual natural disasters. The detection of potential flood-prone areas constitutes one of the fundamental components of the European Natural Disaster Management Policy, directly connected to the European Directive 2007/60. The aim of the present paper is to develop a new methodology that combines geographical information, fuzzy logic and multi-criteria evaluation methods so that the most vulnerable areas are defined. Therefore, ten factors related to geophysical, morphological, climatological/meteorological and hydrological characteristics of the basin were selected. Afterwards, two models were created to detect the areas pronest to flooding. The first model defined the gravitas of each factor using Analytical Hierarchy Process (AHP) and the final map of possible flood spots were created using GIS and Boolean Algebra. The second model made use of the fuzzy logic and GIS combination and a respective map was created. The application area of the aforementioned methodologies was in Ardas basin due to the frequent and important floods that have taken place these last years. Then, the results were compared to the already observed floods. The result analysis shows that both models can detect with great precision possible flood spots. As the fuzzy logic model is less time-consuming, it is considered the ideal model to apply to other areas. The said results are capable of contributing to the delineation of high risk areas and to the creation of successful management plans dealing with floods.Keywords: analytical hierarchy process, flood prone areas, fuzzy logic, geographic information system
Procedia PDF Downloads 3681193 Argumentation Frameworks and Theories of Judging
Authors: Sonia Anand Knowlton
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With the rise of artificial intelligence, computer science is becoming increasingly integrated in virtually every area of life. Of course, the law is no exception. Through argumentation frameworks (AFs), computer scientists have used abstract algebra to structure the legal reasoning process in a way that allows conclusions to be drawn from a formalized system of arguments. In AFs, arguments compete against each other for logical success and are related to one another through the binary operation of the attack. The prevailing arguments make up the preferred extension of the given argumentation framework, telling us what set of arguments must be accepted from a logical standpoint. There have been several developments of AFs since its original conception in the early 90’s in efforts to make them more aligned with the human reasoning process. Generally, these developments have sought to add nuance to the factors that influence the logical success of competing arguments (e.g., giving an argument more logical strength based on the underlying value it promotes). The most cogent development was that of the Extended Argumentation Framework (EAF), in which attacks can themselves be attacked by other arguments, and the promotion of different competing values can be formalized within the system. This article applies the logical structure of EAFs to current theoretical understandings of judicial reasoning to contribute to theories of judging and to the evolution of AFs simultaneously. The argument is that the main limitation of EAFs, when applied to judicial reasoning, is that they require judges to themselves assign values to different arguments and then lexically order these values to determine the given framework’s preferred extension. Drawing on John Rawls’ Theory of Justice, the examination that follows is whether values are lexical and commensurable to this extent. The analysis that follows then suggests a potential extension of the EAF system with an approach that formalizes different “planes of attack” for competing arguments that promote lexically ordered values. This article concludes with a summary of how these insights contribute to theories of judging and of legal reasoning more broadly, specifically in indeterminate cases where judges must turn to value-based approaches.Keywords: computer science, mathematics, law, legal theory, judging
Procedia PDF Downloads 541192 Four-Electron Auger Process for Hollow Ions
Authors: Shahin A. Abdel-Naby, James P. Colgan, Michael S. Pindzola
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A time-dependent close-coupling method is developed to calculate a total, double and triple autoionization rates for hollow atomic ions of four-electron systems. This work was motivated by recent observations of the four-electron Auger process in near K-edge photoionization of C+ ions. The time-dependent close-coupled equations are solved using lattice techniques to obtain a discrete representation of radial wave functions and all operators on a four-dimensional grid with uniform spacing. Initial excited states are obtained by relaxation of the Schrodinger equation in imaginary time using a Schmidt orthogonalization method involving interior subshells. The radial wave function grids are partitioned over the cores on a massively parallel computer, which is essential due to the large memory requirements needed to store the coupled-wave functions and the long run times needed to reach the convergence of the ionization process. Total, double, and triple autoionization rates are obtained by the propagation of the time-dependent close-coupled equations in real-time using integration over bound and continuum single-particle states. These states are generated by matrix diagonalization of one-electron Hamiltonians. The total autoionization rates for each L excited state is found to be slightly above the single autoionization rate for the excited configuration using configuration-average distorted-wave theory. As expected, we find the double and triple autoionization rates to be much smaller than the total autoionization rates. Future work can be extended to study electron-impact triple ionization of atoms or ions. The work was supported in part by grants from the American University of Sharjah and the US Department of Energy. Computational work was carried out at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, California, USA.Keywords: hollow atoms, autoionization, auger rates, time-dependent close-coupling method
Procedia PDF Downloads 1471191 Simulation of Reflectometry in Alborz Tokamak
Authors: S. Kohestani, R. Amrollahi, P. Daryabor
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Microwave diagnostics such as reflectometry are receiving growing attention in magnetic confinement fusionresearch. In order to obtain the better understanding of plasma confinement physics, more detailed measurements on density profile and its fluctuations might be required. A 2D full-wave simulation of ordinary mode propagation has been written in an effort to model effects seen in reflectometry experiment. The code uses the finite-difference-time-domain method with a perfectly-matched-layer absorption boundary to solve Maxwell’s equations.The code has been used to simulate the reflectometer measurement in Alborz Tokamak.Keywords: reflectometry, simulation, ordinary mode, tokamak
Procedia PDF Downloads 4131190 Exponential Stabilization of a Flexible Structure via a Delayed Boundary Control
Authors: N. Smaoui, B. Chentouf
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The boundary stabilization problem of the rotating disk-beam system is a topic of interest in research studies. This system involves a flexible beam attached to the center of a disk, and the control and stabilization of this system have been extensively studied. This research focuses on the case where the center of mass is fixed in an inertial frame, and the rotation of the center is non-uniform. The system is represented by a set of nonlinear coupled partial differential equations and ordinary differential equations. The boundary stabilization problem of this system via a delayed boundary control is considered. We assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. The aim of this research is threefold: First, we demonstrate that the rotating disk-beam system is well-posed in an appropriate functional space. Then, we establish the exponential stability property of the system. Finally, we provide numerical simulations that illustrate the theoretical findings. The research utilizes the semigroup theory to establish the well-posedness of the system. The resolvent method is then employed to prove the exponential stability property. Finally, the finite element method is used to demonstrate the theoretical results through numerical simulations. The research findings indicate that the rotating disk-beam system can be stabilized using a boundary control with a time delay. The proof of stability is based on the resolvent method and a variation of constants formula. The numerical simulations further illustrate the theoretical results. The findings have potential implications for the design and implementation of control strategies in similar systems. In conclusion, this research demonstrates that the rotating disk-beam system can be stabilized using a boundary control with time delay. The well-posedness and exponential stability properties are established through theoretical analysis, and these findings are further supported by numerical simulations. The research contributes to the understanding and practical application of control strategies for flexible structures, providing insights into the stability of rotating disk-beam systems.Keywords: rotating disk-beam, delayed force control, delayed moment control, torque control, exponential stability
Procedia PDF Downloads 671189 Electromagnetic Tuned Mass Damper Approach for Regenerative Suspension
Authors: S. Kopylov, C. Z. Bo
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This study is aimed at exploring the possibility of energy recovery through the suppression of vibrations. The article describes design of electromagnetic dynamic damper. The magnetic part of the device performs the function of a tuned mass damper, thereby providing both energy regeneration and damping properties to the protected mass. According to the theory of tuned mass damper, equations of mathematical models were obtained. Then, under given properties of current system, amplitude frequency response was investigated. Therefore, main ideas and methods for further research were defined.Keywords: electromagnetic damper, oscillations with two degrees of freedom, regeneration systems, tuned mass damper
Procedia PDF Downloads 2031188 Enhanced Tensor Tomographic Reconstruction: Integrating Absorption, Refraction and Temporal Effects
Authors: Lukas Vierus, Thomas Schuster
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A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions
Procedia PDF Downloads 381187 Multivalued Behavior for a Two-Level System Using Homotopy Analysis Method
Authors: Angelo I. Aquino, Luis Ma. T. Bo-ot
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We use the Homotopy Analysis Method (HAM) to solve the system of equations modeling the two-level system and extract results which will pinpoint to turbulent behavior. We look at multi-valued solutions as indicative of turbulence or turbulent-like behavior. We take dierent specic cases which result in multi-valued velocities. The solutions are in series form and application of HAM ensures convergence in some region.Keywords: multivalued solutions, homotopy analysis method, two-level system, equation
Procedia PDF Downloads 5891186 Analysis of the Inverse Kinematics for 5 DOF Robot Arm Using D-H Parameters
Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale
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This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories
Procedia PDF Downloads 1901185 Chaos in a Stadium-Shaped 2-D Quantum Dot
Authors: Roger Yu
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A numerical scheme has been developed to solve wave equations for chaotic systems such as stadium-shaped cavity. The same numerical method can also be used for finding wave properties of rectangle cavities with randomly placed obstacles. About 30k eigenvalues have been obtained accurately on a normal circumstance. For comparison, we also initiated an experimental study which determines both eigenfrequencies and eigenfunctions of a stadium-shaped cavity using pulse and normal mode analyzing techniques. The acoustic cavity was made adjustable so that the transition from nonchaotic (circle) to chaotic (stadium) waves can be investigated.Keywords: quantum dot, chaos, numerical method, eigenvalues
Procedia PDF Downloads 1121184 Multidimensional Integral and Discrete Opial–Type Inequalities
Authors: Maja Andrić, Josip Pečarić
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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality
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