Search results for: oscillatory singular integral

Authors: V. Tabrizi, A. Vali, R. GHasemi, V. Behnamgol

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In this article, a nonlinear model of an under actuated six degrees of freedom (6 DOF) quadrotor UAV is derived on the basis of the Newton-Euler formula. The derivation comprises determining equations of the motion of the quadrotor in three dimensions and approximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics. The robust nonlinear control strategy includes a smooth second order non-singular terminal sliding mode control which is applied to stabilizing this model. The control method is on the basis of super twisting algorithm for removing the chattering and producing smooth control signal. Also, nonsingular terminal sliding mode idea is used for introducing a nonlinear sliding variable that guarantees the finite time convergence in sliding phase. Simulation results show that the proposed algorithm is robust against uncertainty or disturbance and guarantees a fast and precise control signal.

Keywords: quadrotor UAV, nonsingular terminal sliding mode, second order sliding mode t, electronics, control, signal processing

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Authors: Iftikhar Ahmad, A. Benallegue, A. El Hadri

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In this paper, we have proposed an observer for the reconstruction and a control law for the rejection application of unknown bounded external disturbance in a dynamical system. The strategy of both the observer and the controller is designed like a second order sliding mode with a proportional-integral (PI) term. Lyapunov theory is used to prove the exponential convergence and stability. Simulations results are given to show the performance of this method.

Keywords: non-linear systems, sliding mode observer, disturbance rejection, nonlinear control

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Authors: Haythem H. Abdullah, Hesham Elkady

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With the fast increase in radio frequency identification (RFID) applications such as medical recording, library management, etc., the limitation of active tags stems from its need to external batteries as well as passive or active chips. The chipless RFID tag reduces the cost to a large extent but at the expense of utilizing the spectrum. The reduction of the cost of chipless RFID is due to the absence of the chip itself. The identification is done by utilizing the spectrum in such a way that the frequency response of the tags consists of some resonance frequencies that represent the bits. The system capacity is decided by the number of resonators within the pre-specified band. It is important to find a solution to enhance the spectrum utilization when using chipless RFID. Target identification is a process that results in a decision that a specific target is present or not. Several target identification schemes are present, but one of the most successful techniques in radar target identification in the oscillatory region is the extinction pulse technique (E-Pulse). The E-Pulse technique is used to identify targets via its characteristics (natural) modes. By introducing an innovative solution for chipless RFID reader and tag designs, the spectrum utilization goes to the optimum case. In this paper, a novel capacity enhancement scheme based on the E-pulse technique is introduced to improve the performance of the chipless RFID system.

Keywords: chipless RFID, E-pulse, natural modes, resonators

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Authors: Hosein Falahaty, Hitoshi Gotoh, Abbas Khayyer

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Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

Keywords: Hamilton's principle of least action, particle-based method, hyper-elasticity, analysis of stability

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Authors: Ci Lin, Tet Yeap, Iluju Kiringa

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This paper introduces the subspace rotation algorithm (SRA) to train the Restricted Hopfield Network (RHN) as an auto-associative memory. Subspace rotation algorithm is a gradient-free subspace tracking approach based on the singular value decomposition (SVD). In comparison with Backpropagation Through Time (BPTT) on training RHN, it is observed that SRA could always converge to the optimal solution and BPTT could not achieve the same performance when the model becomes complex, and the number of patterns is large. The AUTS case study showed that the RHN model trained by SRA could achieve a better structure of attraction basin with larger radius(in general) than the Hopfield Network(HNN) model trained by Hebbian learning rule. Through learning 10000 patterns from MNIST dataset with RHN models with different number of hidden nodes, it is observed that an several components could be adjusted to achieve a balance between recovery accuracy and noise resistance.

Keywords: hopfield neural network, restricted hopfield network, subspace rotation algorithm, hebbian learning rule

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Authors: M. Laura Vazquez Maggio, Lilia Dominguez Villalobos, Jan Luka Frey

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This paper contributes to the understanding of the dynamic and the relational nature of identities formation among skilled middle-class migrants. Following the idea that identities are never singular, multifaceted and have a necessarily processual character, the authors specifically analyze three dimensions of the identity of qualified Mexican migrants in the US and the interplay between them. Drawing on semi-structured interviews with skilled Mexican middle-class migrants in the US, the paper explores how skilled Mexican migrants preserve their ethno-national identity (their ‘Mexicanness’) in reaction to a hostile socio-political reception context in the US. It further shows how these migrants recreate their class identity and show tendencies to distance themselves from what they perceive as lower-class Mexican migrants and the dominant popular Mexican and Latin-American cultural expressions. In a final step, it examines how the lived experience of migration itself impacts the migrants’ identities, their concept of self and feelings/modes of being and belonging.

Keywords: ethno-national identity, middle class identity, middle-class migration, migrants’ identity, skilled migration

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Authors: Zarine Avetisyan

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The paradigm of Modern Linguistics incorporates disciplines which allow to analyze both language and discourse units and to demonstrate the multi-layeredness of lingo-cultural consciousness. By implementing lingo-cognitive approach to discourse and communication studies, the present paper tries to create the integral linguistic picture of the concept of joy and to analyze the lexico-semantic groups and relevant lexico-semantic variants of its realization in the context of Modern English fiction.

Keywords: concept of joy, lexico-semantic variant, semantic sign, cognition

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Authors: Ali Yasin, Ali Kamran, Muhammad Safdar

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In order to reduce the hefty cost involved in terms of time and project cost, the development and application of advanced numerical tools to address the burn-back analysis problem in solid rocket motor design and development is the need of time. Several advanced numerical schemes have been developed in recent times, but their usage in the design of propellant grain of solid rocket motors is very rare. In this paper, an advanced numerical technique named the Level-Set method has been utilized for the burn-back analysis of star grain to study the effect of geometrical parameters on ballistic performance indicators such as solid loading, neutrality, and sliver percentage. In the level set technique, simple finite difference methods may fail quickly and require more sophisticated non-oscillatory schemes for feasible long-time simulation. For internal ballistic calculations, a simplified equilibrium pressure method is utilized. Preliminary results of the operative conditions, for all the combustion time, of star grain burn-back using level set techniques are compared with published results using CAD technique to test the developed numerical model.

Keywords: solid rocket motor, internal ballistic, level-set technique, star grain

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Authors: Bianca Suárez Puerta

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Multimodal discourse refers to a method of study the media continuum between reality, screens as a device, audience, author, and media as a production from the audience. For this study we used semantic differential, a method proposed in the sixties by Osgood, Suci and Tannenbaum, starts from the assumption that under each particular way of perceiving the world, in each singular idea, there is a common cultural meaning that organizes experiences. In relation to these shared symbolic dimension, this method has had significant results, as it focuses on breaking down the meaning of certain significant acts into series of statements that place the subjects in front of some concepts. In Colombia, in 2016, a tool was designed to measure the meaning of a multimodal production, specially the acts of sense of transmedia productions that managed to receive funds from the Ministry of ICT of Colombia, and also, to analyze predictable patterns that can be found in calls and funds aimed at the production of culture in Colombia, in the context of the peace agreement, as a request for expressions from a hegemonic place, seeking to impose a worldview.

Keywords: semantic differential, semiotics, transmedia, critical analysis of discourse

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Authors: Inas S. Khayal, Weiping Zhou, Jonathan Skinner

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Healthcare delivery systems around the world are in crisis. The need to improve health outcomes while decreasing healthcare costs have led to an imminent call to action to transform the healthcare delivery system. While Bioinformatics and Biomedical Engineering have primarily focused on biological level data and biomedical technology, there is clear evidence of the importance of the delivery of care on patient outcomes. Classic singular decomposition approaches from reductionist science are not capable of explaining complex systems. Approaches and methods from systems science and systems engineering are utilized to structure healthcare delivery system data. Specifically, systems architecture is used to develop a multi-scale and multi-dimensional characterization of the healthcare delivery system, defined here as the Healthcare Delivery System Knowledge Base. This paper is the first to contribute a new method of structuring and visualizing a multi-dimensional and multi-scale healthcare delivery system using systems architecture in order to better understand healthcare delivery.

Keywords: health informatics, systems thinking, systems architecture, healthcare delivery system, data analytics

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Authors: Ali Raheli, Rahim Habibifar, Behzad Mohammadi-Alasti, Mahdi Abbasgholipour

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This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated.

Keywords: FGM, MEMS, nonlinear vibration, electrical, dynamic pull-in voltage

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Bonchan Koo, Junhee Han, Dohyung Lee

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The research attempts to evaluate the accuracy and efficiency of a design optimization procedure which combines wavelets-based solution algorithm and proper orthogonal decomposition (POD) database management technique. Aerodynamic design procedure calls for high fidelity computational fluid dynamic (CFD) simulations and the consideration of large number of flow conditions and design constraints. Even with significant computing power advancement, current level of integrated design process requires substantial computing time and resources. POD reduces the degree of freedom of full system through conducting singular value decomposition for various field simulations. For additional efficiency improvement of the procedure, adaptive wavelet technique is also being employed during POD training period. The proposed design procedure was applied to the optimization of wing aerodynamic performance. Throughout the research, it was confirmed that the POD/wavelets design procedure could significantly reduce the total design turnaround time and is also able to capture all detailed complex flow features as in full order analysis.

Keywords: POD (Proper Orthogonal Decomposition), wavelets, CFD, design optimization, ROM (Reduced Order Model)

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Authors: Elisa Y. M. Ang, Teng Yong Ng, Jingjie Yeo, Rongming Lin, Zishun Liu, K. R. Geethalakshmi

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By stacking carbon nanotubes (CNT) one on top of another, single layer CNT arrays can perform water-salt separation with ultra-high permeability and selectivity. Such outer-wall CNT slit membrane is named as the transverse flow CNT membrane. By adjusting the slit size between neighboring CNTs, the membrane can be configured to sieve out different solutes, right down to the separation of monovalent salt ions from water. Molecular dynamics (MD) simulation results show that the permeability of transverse flow CNT membrane is more than two times that of conventional axial-flow CNT membranes, and orders of magnitude higher than current reverse osmosis membrane. In addition, by carrying out MD simulations with different CNT size, it was observed that the variance in desalination performance with CNT size is small. This insensitivity of the transverse flow CNT membrane’s performance to CNT size is a distinct advantage over axial flow CNT membrane designs. Not only does the membrane operate well under constant pressure desalination operation, but MD simulations further indicate that oscillatory operation can further enhance the membrane’s desalination performance, making it suitable for operation such as electrodialysis reversal. While there are still challenges that need to be overcome, particularly on the physical fabrication of such membrane, it is hope that this versatile membrane design can bring the idea of using low dimensional structures for desalination closer to reality.

Keywords: carbon nanotubes, membrane desalination, transverse flow carbon nanotube membrane, molecular dynamics

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Authors: Nishant Parashar, Sawan S. Sinha, Balaji Srinivasan

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We perform an investigation of the unclosed terms in the evolution equation of the velocity gradient tensor (VGT) in compressible decaying turbulent flow. Velocity gradients in a compressible turbulent flow field influence several important nonlinear turbulent processes like cascading and intermittency. In an attempt to understand the dynamics of the velocity gradients various researchers have tried to model the unclosed terms in the evolution equation of the VGT. The existing models proposed for these unclosed terms have limited applicability. This is mainly attributable to the complex structure of the higher order gradient terms appearing in the evolution equation of VGT. We investigate these higher order gradients using the data from direct numerical simulation (DNS) of compressible decaying isotropic turbulent flow. The gas kinetic method aided with weighted essentially non-oscillatory scheme (WENO) based flow- reconstruction is employed to generate DNS data. By applying neural-network to the DNS data, we map the structure of the unclosed higher order gradient terms in the evolution of the equation of the VGT with VGT itself. We validate our findings by performing alignment based study of the unclosed higher order gradient terms obtained using the neural network with the strain rate eigenvectors.

Keywords: compressible turbulence, neural network, velocity gradient tensor, direct numerical simulation

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Authors: Juland D. Salayo

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With numerous innovations introduced in the Philippine educational system, the country’s struggle of materializing its national goal of transforming lives ends with great loss. Many agree that the failure to emerge the integral values of the program, framework and the implementers impedes realization. Employing a descriptive-correlational method, it aimed to determine the value clusters of the Grade 9 teachers as assessed by themselves and by the students, the significant difference of the assessed values and the significant difference on the values based on their profile. Respondents were composed of sixty-nine (69) teachers and three hundred forty (340) students using simple random sampling. Through a survey-questionnaire, the study revealed that the teachers have high regards on their self-reliance, honesty and trustworthiness, obedience, politeness and respect and self-discipline and spirituality. In contrast, they have ranked the following values fairly: justice and fairness, courage, responsibility and punctuality and nationalism and patriotism. Having assessed by the students, they have highly regarded their teachers’ self-reliance, responsibility and punctuality, obedience, politeness and respect and fair play and sportsmanship. On the other hand, the student-respondents made a low assessment on the level of the teachers’ justice and fairness, nationalism and patriotism, honesty and trustworthiness and excellence. Using t-test, it showed that there is a significant difference between the assessments of the respondents. Finally, among the demographic profiles, only civil status and age rejected the hypothesis. The following were recommended: provide educators value-enhancement trainings and conferences, organize value-oriented organizations and activities, and make intensive value-campaigns heightening the low-assessed values. Thus, a Revised Values Education Program (RVEP) was made to further meet the objectives of the program, address the needs of its clienteles, and responding to the demands of both education and society towards excellence in service, social and economic revolution, and constructive national goals which are based from integral values.

Keywords: values, value clusters, values education program, values education, teachers' assessed values

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Authors: Eugene Stepanov, Arkadi Ponossov

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Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities.

Keywords: hybrid feedback control, ill-posed problems, singular perturbation analysis, step-like nonlinearities

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Authors: Rashmi Dubey

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The study aims at investigating the onset of thermal convection in an inclined porous layer saturated with a non-Newtonian fluid. The layer is infinitely extended and has a finite width confined between two boundaries with constant pressure conditions, where the lower one is maintained at a higher temperature. Over the years, this area of research has attracted many scientists and researchers, for it has a plethora of applications in the fields of sciences and engineering, such as in civil engineering, geothermal sites, petroleum industries, etc.Considering the possibilities in a practical scenario, an inclined porous layer is considered, which can be used to develop a generalized model applicable to any inclination. Using the isobaric boundaries, the hydrodynamic boundary conditions are derived for the power-law model and are used to obtain the basic state flow. The convection in the basic state flow is driven by the thermal buoyancy in the flow system and is carried away further due to hydrodynamic boundaries. A linear stability analysis followed by a normal-mode analysis is done to investigate the onset of convection in the buoyancy-driven flow. The analysis shows that the convective instability is always initiated by the non-traveling modes for the Newtonian fluid, but prevails in the form of oscillatory modes, for up to a certain inclination of the porous layer. However, different behavior is observed for the dilatant and pseudoplastic fluids.

Keywords: thermal convection, linear stability, porous media flow, Inclined porous layer

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Authors: Jana Abu Ahmada, Zaineb Mohamed, Ilyasse Aksikas

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The linear quadratic control system of hyperbolic first order partial differential equations (PDEs) are presented. The aim of this research is to control chemical reactions. This is achieved by converting the PDEs system to ordinary differential equations (ODEs) using the method of characteristics to reduce the system to control it by using the integral reinforcement learning. The designed controller is applied to a catalytic cracking reactor. Background—Transport-Reaction systems cover a large chemical and bio-chemical processes. They are best described by nonlinear PDEs derived from mass and energy balances. As a main application to be considered in this work is the catalytic cracking reactor. Indeed, the cracking reactor is widely used to convert high-boiling, high-molecular weight hydrocarbon fractions of petroleum crude oils into more valuable gasoline, olefinic gases, and others. On the other hand, control of PDEs systems is an important and rich area of research. One of the main control techniques is feedback control. This type of control utilizes information coming from the system to correct its trajectories and drive it to a desired state. Moreover, feedback control rejects disturbances and reduces the variation effects on the plant parameters. Linear-quadratic control is a feedback control since the developed optimal input is expressed as feedback on the system state to exponentially stabilize and drive a linear plant to the steady-state while minimizing a cost criterion. The integral reinforcement learning policy iteration technique is a strong method that solves the linear quadratic regulator problem for continuous-time systems online in real time, using only partial information about the system dynamics (i.e. the drift dynamics A of the system need not be known), and without requiring measurements of the state derivative. This is, in effect, a direct (i.e. no system identification procedure is employed) adaptive control scheme for partially unknown linear systems that converges to the optimal control solution. Contribution—The goal of this research is to Develop a characteristics-based optimal controller for a class of hyperbolic PDEs and apply the developed controller to a catalytic cracking reactor model. In the first part, developing an algorithm to control a class of hyperbolic PDEs system will be investigated. The method of characteristics will be employed to convert the PDEs system into a system of ODEs. Then, the control problem will be solved along the characteristic curves. The reinforcement technique is implemented to find the state-feedback matrix. In the other half, applying the developed algorithm to the important application of a catalytic cracking reactor. The main objective is to use the inlet fraction of gas oil as a manipulated variable to drive the process state towards desired trajectories. The outcome of this challenging research would yield the potential to provide a significant technological innovation for the gas industries since the catalytic cracking reactor is one of the most important conversion processes in petroleum refineries.

Keywords: PDEs, reinforcement iteration, method of characteristics, riccati equation, cracking reactor

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Authors: Prawal Sinha, Peeyush Singh, Pravir Dutt

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Problems in elastohydrodynamic lubrication have attracted a lot of attention in the last few decades. Solving a two-dimensional problem has always been a big challenge. In this paper, a new discontinuous finite volume method (DVM) for two-dimensional point contact Elastohydrodynamic Lubrication (EHL) problem has been developed and analyzed. A complete algorithm has been presented for solving such a problem. The method presented is robust and easily parallelized in MPI architecture. GMRES technique is implemented to solve the matrix obtained after the formulation. A new approach is followed in which discontinuous piecewise polynomials are used for the trail functions. It is natural to assume that the advantages of using discontinuous functions in finite element methods should also apply to finite volume methods. The nature of the discontinuity of the trail function is such that the elements in the corresponding dual partition have the smallest support as compared with the Classical finite volume methods. Film thickness calculation is done using singular quadrature approach. Results obtained have been presented graphically and discussed. This method is well suited for solving EHL point contact problem and can probably be used as commercial software.

Keywords: elastohydrodynamic, lubrication, discontinuous finite volume method, GMRES technique

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Authors: S. Junaid S. Qazi, Denice C. Bay, Raymond Chew, Raymond J. Turner

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EmrE, a member of the small multidrug resistance protein family in bacteria is considered to be the archetypical member of its family. It confers host resistance to a wide variety of quaternary cation compounds (QCCs) driven by proton motive force. Generally, purification yield is a challenge in all membrane proteins because of the difficulties in their expression, isolation and solubilization. EmrE is extremely hydrophobic which make the purification yield challenging. We have purified EmrE protein using two different approaches: organic solvent membrane extraction and hexahistidine (his6) tagged Ni-affinity chromatographic methods. We have characterized changes present between ligand affinity of untagged and his6-tagged EmrE proteins in similar membrane mimetic environments using biophysical experimental techniques. Purified proteins were solubilized in a buffer containing n-dodecyl-β-D-maltopyranoside (DDM) and the conformations in the proteins were explored in the presence of four QCCs, methyl viologen (MV), ethidium bromide (EB), cetylpyridinium chloride (CTP) and tetraphenyl phosphonium (TPP). SDS-Tricine PAGE and dynamic light scattering (DLS) analysis revealed that the addition of QCCs did not induce higher multimeric forms of either proteins at all QCC:EmrE molar ratios examined under the solubilization conditions applied. QCC binding curves obtained from the Trp fluorescence quenching spectra, gave the values of dissociation constant (Kd) and maximum specific one-site binding (Bmax). Lower Bmax values to QCCs for his6-tagged EmrE shows that the binding sites remained unoccupied. This lower saturation suggests that the his6-tagged versions provide a conformation that prevents saturated binding. Our data demonstrate that tagging an integral membrane protein can significantly influence the protein.

Keywords: small multidrug resistance (SMR) protein, EmrE, integral membrane protein folding, quaternary ammonium compounds (QAC), quaternary cation compounds (QCC), nickel affinity chromatography, hexahistidine (His6) tag

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Authors: Raef Cherif, Houssine Bakkali, Wafaa El Khatiri, Yacine Yaddaden

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The analysis of how vibrations are transmitted between components is required in many engineering applications. Transfer path analysis (TPA) has been a valuable engineering tool for solving Noise, Vibration, and Harshness (NVH problems using sub-structuring applications. The most challenging part of a TPA analysis is estimating the equivalent forces at the contact points between the active and the passive side. Component TPA in situ Method calculates these forces by inverting the frequency response functions (FRFs) measured at the passive subsystem, relating the motion at indicator points to forces at the interface. However, matrix inversion could pose problems due to the ill-conditioning of the matrices leading to inaccurate results. This paper establishes a TPA model for an academic system consisting of two plates linked by four springs. A numerical study has been performed to improve the interface forces identification. Several parameters are studied and discussed, such as the singular value rejection and the number and position of indicator points chosen and used in the inversion matrix.

Keywords: transfer path analysis, matrix inverse method, indicator points, SVD decomposition

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Authors: James Adewale, Joshua Sunday

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In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods.

Keywords: predictor, corrector, collocation, interpolation, approximate solution, independent solution, zero stable, consistent, convergent

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Authors: Jinlai Bian, Zailin Yang, Guanxixi Jiang, Xinzhu Li

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The problem of elastic wave propagation in inhomogeneous medium has always been a classic problem. Due to the frequent occurrence of earthquakes, many economic losses and casualties have been caused, therefore, to prevent earthquake damage to people and reduce damage, this paper studies the dynamic response around the circular inclusion in the whole space with inhomogeneous modulus, the inhomogeneity of the medium is reflected in the shear modulus of the medium with the spatial position, and the density is constant, this method can be used to solve the problem of the underground buried pipeline. Stress concentration phenomena are common in aerospace and earthquake engineering, and the dynamic stress concentration factor (DSCF) is one of the main factors leading to material damage, one of the important applications of the theory of elastic dynamics is to determine the stress concentration in the body with discontinuities such as cracks, holes, and inclusions. At present, the methods include wave function expansion method, integral transformation method, integral equation method and so on. Based on the complex function method, the Helmholtz equation with variable coefficients is standardized by using conformal transformation method and wave function expansion method, the displacement and stress fields in the whole space with circular inclusions are solved in the complex coordinate system, the unknown coefficients are solved by using boundary conditions, by comparing with the existing results, the correctness of this method is verified, based on the superiority of the complex variable function theory to the conformal transformation, this method can be extended to study the inclusion problem of arbitrary shapes. By solving the dynamic stress concentration factor around the inclusions, the influence of the inhomogeneous parameters of the medium and the wavenumber ratio of the inclusions to the matrix on the dynamic stress concentration factor is analyzed. The research results can provide some reference value for the evaluation of nondestructive testing (NDT), oil exploration, seismic monitoring, and soil-structure interaction.

Keywords: circular inclusions, complex variable function, dynamic stress concentration factor (DSCF), inhomogeneous medium

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Authors: A.Chen Chao-Chang, Phong Pham-Quoc

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Chemical-mechanical polishing (CMP) process has been widely applied on fabricating integrated circuits (IC) with a soft polishing pad combined with slurry composed of micron or nano-scaled abrasives for generating chemical reaction to remove substrate or film materials from wafer. During CMP process, pad uniformity usually works as a datum surface of wafer planarization and pad asperities can dominate the microscopic pad-slurry-wafer interaction. However, pad topography can be changed by related mechanism factors of CMP and it needs to be re-conditioned or dressed by a diamond dresser of well-distributed diamond grits on a disc surface. It is still very complicated to analyze and understand kinematic of diamond dressing process under the effects of input variables including oscillatory of diamond dresser and rotation speed ratio between the pad and the diamond dresser. This paper has developed a generic geometric model to clarify the kinematic modeling of diamond dressing processes such as dresser/pad motion, pad cutting locus, the relative velocity of the diamond abrasive grits on pad surface, and overlap of cutting for prediction of pad surface topography. Simulation results focus on comparing and analysis kinematics of the diamond dressing on certain CMP tools. Results have shown the significant parameters for diamond dressing process and also discussed. Future study can apply on diamond dresser design and experimental verification of pad dressing process.

Keywords: kinematic modeling, diamond dresser, pad cutting locus, CMP

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

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So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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Authors: Adrian W. Egger, Savvas P. Triantafyllou, Eleni N. Chatzi

Abstract:

The scaled boundary finite element method (SBFEM) is a semi-analytical numerical method, which introduces a scaling center in each element’s domain, thus transitioning from a Cartesian reference frame to one resembling polar coordinates. Consequently, an analytical solution is achieved in radial direction, implying that only the boundary need be discretized. The only limitation imposed on the resulting polygonal elements is that they remain star-convex. Further arbitrary p- or h-refinement may be applied locally in a mesh. The polygonal nature of SBFEM elements has been exploited in quadtree meshes to alleviate all issues conventionally associated with hanging nodes. Furthermore, since in 2D this results in only 16 possible cell configurations, these are precomputed in order to accelerate the forward analysis significantly. Any cells, which are clipped to accommodate the domain geometry, must be computed conventionally. However, since SBFEM permits polygonal elements, significantly coarser meshes at comparable accuracy levels are obtained when compared with conventional quadtree analysis, further increasing the computational efficiency of this scheme. The generalized stress intensity factors (gSIFs) are computed by exploiting the semi-analytical solution in radial direction. This is initiated by placing the scaling center of the element containing the crack at the crack tip. Taking an analytical limit of this element’s stress field as it approaches the crack tip, delivers an expression for the singular stress field. By applying the problem specific boundary conditions, the geometry correction factor is obtained, and the gSIFs are then evaluated based on their formal definition. Since the SBFEM solution is constructed as a power series, not unlike mode superposition in FEM, the two modes contributing to the singular response of the element can be easily identified in post-processing. Compared to the extended finite element method (XFEM) this approach is highly convenient, since neither enrichment terms nor a priori knowledge of the singularity is required. Computation of the gSIFs by SBFEM permits exceptional accuracy, however, when combined with hybrid quadtrees employing linear elements, this does not always hold. Nevertheless, it has been shown that crack propagation schemes are highly effective even given very coarse discretization since they only rely on the ratio of mode one to mode two gSIFs. The absolute values of the gSIFs may still be subject to large errors. Hence, we propose a post-processing scheme, which minimizes the error resulting from the approximation space of the cracked element, thus limiting the error in the gSIFs to the discretization error of the quadtree mesh. This is achieved by h- and/or p-refinement of the cracked element, which elevates the amount of modes present in the solution. The resulting numerical description of the element is highly accurate, with the main error source now stemming from its boundary displacement solution. Numerical examples show that this post-processing procedure can significantly improve the accuracy of the computed gSIFs with negligible computational cost even on coarse meshes resulting from hybrid quadtrees.

Keywords: linear elastic fracture mechanics, generalized stress intensity factors, scaled finite element method, hybrid quadtrees

Procedia PDF Downloads 114

Authors: Vernie C. Convicto, Henry P. Aringa, Wilson I. Barredo

Abstract:

This study presents a conformational model of the helical structures of globular protein particularly ferritin in the framework of white noise path integral formulation by using Associated Legendre functions, Bessel and convolution of Bessel and trigonometric functions as modulating functions. The model incorporates chirality features of proteins and their helix-turn-helix sequence structural motif.

Keywords: globular protein, modulating function, white noise, winding probability

Procedia PDF Downloads 444

Authors: Pradyumna R., Sridhar S., A. Satyanarayana, Alok S. Chauhan, Baig M. A. H.

Abstract:

Modern turbine engines for aerospace applications need precision investment cast components such as integrally cast rotors and stators, for their hot end turbine stages. Traditionally, these turbines are used as starter engines. In recent times, such engines are also used for strategic missile applications. The rotor/stator castings consist of a central hub (shrouded in some designs) over which a number of aerofoil shaped blades are located. Since these components cannot be machined, investment casting is the only available route for manufacture and hence stringent dimensional aerospace quality has to be in-built in the casting process itself. In the process of investment casting, pattern generation by injection of wax into dedicated dies/moulds is the first critical step. Traditional approach deals in producing individual blades with hub/shroud features through wax injection and assembly of a set of such injected patterns onto a dedicated and precisely manufactured fixture to wax-weld and generate an integral wax pattern, a process known as the ‘segmental approach’. It is possible to design a single-injection die with retractable metallic inserts in the case of untwisted blades of stator patterns without the shroud. Such an approach is also possible for twisted blades of rotors with highly complex design of inter-blade inserts and retraction mechanisms. DMRL has for long established methods and procedures for the above to successfully supply precision castings for various defence related projects. In recent times, urea based soluble insert approach has also been successfully applied to overcome the need to design and manufacture a precision assembly fixture, leading to substantial reduction in component development times. Present paper deals in length various approaches tried and established at DMRL to generate precision wax patterns for aerospace quality turbine rotors and stators. In addition to this, the importance of simulation in solving issues related to wax injection is also touched upon.

Keywords: die/mold and fixtures, integral rotor/stator, investment casting, wax patterns, simulation

Procedia PDF Downloads 320