Search results for: numerical optimisation

Authors: Omid Heydarnia, Akbar Allahverdizadeh, Behnam Dadashzadeh, M. R. Sayyed Noorani

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Underactuated biped robots control is one of the interesting topics in robotics. The main difficulties are its highly nonlinear dynamics, open-loop instability, and discrete event at the end of the gait. One of the methods to control underactuated systems is the partial feedback linearization, but it is not robust against uncertainties and disturbances that restrict its performance to control biped walking and running. In this paper, fuzzy partial feedback linearization is presented to overcome its drawback. Numerical simulations verify the effectiveness of the proposed method to generate stable and robust biped walking and running gaits.

Keywords: underactuated system, biped robot, fuzzy control, partial feedback linearization

Procedia PDF Downloads 343

Authors: Babak Daneshvar Rouyendegh

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The aim of this study is to develop and describe a new methodology for the Multi-Criteria Decision-Making (MCDM) problem using Intuitionistic Fuzzy Elimination Et Choix Traduisant La REalite (IFELECTRE) model. The proposed models enable Decision-Makers (DMs) on the assessment and use Intuitionistic Fuzzy numbers (IFN). A numerical example is provided to demonstrate and clarify the proposed analysis procedure. Also, an empirical experiment is conducted to validation the effectiveness.

Keywords: Decision-Makers (DMs), Multi-Criteria Decision-Making (MCDM), Intuitionistic Fuzzy Elimination Et Choix Traduisant La REalite (IFELECTRE), Intuitionistic Fuzzy Numbers (IFN)

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Authors: Jurij Tasinkiewicz

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The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wave beam both in elevation and azimuth. In this paper, a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: beamforming, transducer array, BIS-expansion, piezoelectric layer

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Authors: Eugen Rusu

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The objective of the work proposed is to perform an analysis of the wave conditions in the Black Sea basin. This is especially focused on the spatial and temporal occurrences and on the dynamics of the most extreme storms in the context of the climate changes. A numerical modelling system, based on the spectral phase averaged wave model SWAN, has been implemented and validated against both in situ measurements and remotely sensed data, all along the sea. Moreover, a successive correction method for the assimilation of the satellite data has been associated with the wave modelling system. This is based on the optimal interpolation of the satellite data. Previous studies show that the process of data assimilation improves considerably the reliability of the results provided by the modelling system. This especially concerns the most sensitive cases from the point of view of the accuracy of the wave predictions, as the extreme storm situations are. Following this numerical approach, it has to be highlighted that the results provided by the wave modelling system above described are in general in line with those provided by some similar wave prediction systems implemented in enclosed or semi-enclosed sea basins. Simulations of this wave modelling system with data assimilation have been performed for the 30-year period 1987-2016. Considering this database, the next step was to analyze the intensity and the dynamics of the higher storms encountered in this period. According to the data resulted from the model simulations, the western side of the sea is considerably more energetic than the rest of the basin. In this western region, regular strong storms provide usually significant wave heights greater than 8m. This may lead to maximum wave heights even greater than 15m. Such regular strong storms may occur several times in one year, usually in the wintertime, or in late autumn, and it can be noticed that their frequency becomes higher in the last decade. As regards the case of the most extreme storms, significant wave heights greater than 10m and maximum wave heights close to 20m (and even greater) may occur. Such extreme storms, which in the past were noticed only once in four or five years, are more recent to be faced almost every year in the Black Sea, and this seems to be a consequence of the climate changes. The analysis performed included also the dynamics of the monthly and annual significant wave height maxima as well as the identification of the most probable spatial and temporal occurrences of the extreme storm events. Finally, it can be concluded that the present work provides valuable information related to the characteristics of the storm conditions and on their dynamics in the Black Sea. This environment is currently subjected to high navigation traffic and intense offshore and nearshore activities and the strong storms that systematically occur may produce accidents with very serious consequences.

Keywords: Black Sea, extreme storms, SWAN simulations, waves

Procedia PDF Downloads 239

Authors: Corbel Camille, Le Cerf Flora, Capriz Françoise, Vaillant-Ciszewicz Anne-Julie, Breaud Jean, Guerin Olivier, Corveleyn Xavier

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Background: The medical environment can generate stressful and anxiety-provoking situations for patients, particularly during painful care procedures for the older population. These stressful environments have deleterious effects on the quality of care and can even put the patient at risk and set the care team up for failure. The search for a solution is, therefore, imperative. The development of new technologies, such as virtual reality (VR), seems to be an answer to this problem. Objectives: The objective of this study is to compare the effects of virtual reality on pain and anxiety when caring for older hospitalized people with the effects of usual care. More precisely, different individual factors (age, cognitive level, individual preferences, etc.) and different virtual reality universes (personalized or non-personalized) are studied to understand the role of these factors in reducing pain and anxiety during care procedures. The aim of this study is to improve the quality of life of patients and caregivers in their work environment. Method: This mono-centered, randomized, controlled study was conducted from September 2023 to September 2024 on 120 participants recruited from the geriatric departments of the Cimiez Hospital, Nice, France. Participants are randomized into three groups: a control group, a personalized VR group and a non-personalized VR group. Each participant is followed during a painful care session. Data are collected before, during and after the care, using measures of pain (Algoplus and numerical scale) and anxiety (Hospital anxiety scale and numerical scale). Physiological assessments with an oximeter are also performed to collect both heart and respiratory rate measurements. The implementation of the care will be assessed among healthcare providers to evaluate its effects on the difficulty and fatigue associated with the care. Additionally, a questionnaire (System Usability Scale) will be administered at the conclusion of the study to determine the willingness of healthcare providers to integrate VR into their daily care practices. Result: The preliminary results indicate significant effects on anxiety (p=.001) and pain (p=<.001) following the VR intervention during care, as compared to the control group. Conclusion: The preliminary results suggest that VRI appears to be a suitable and effective method for reducing anxiety and pain among older hospitalized individuals compared with standard care. Finally, the experiences of healthcare professionals involved will also be considered to assess the impact of these interventions on working conditions and patient support.

Keywords: anxiety, care, pain, older adults, virtual reality

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Authors: Amir Nazemi, Milad Ramezankhani, Marian Kӧrber, Abbas S. Milani

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The excellent strength to weight ratio of woven fabric composites, along with their high formability, is one of the primary design parameters defining their increased use in modern manufacturing processes, including those in aerospace and automotive. However, for emerging automated preform processes under the smart manufacturing paradigm, complex geometries of finished components continue to bring several challenges to the designers to cope with manufacturing defects on site. Wrinklinge. g. is a common defectoccurring during the forming process and handling of semi-finished textile composites. One of the main reasons for this defect is the weak bending stiffness of fibers in unconsolidated state, causing excessive relative motion between them. Further challenges are represented by the automated handling of large-area fiber blanks with specialized gripper systems. For fabric composites forming simulations, the finite element (FE)method is a longstanding tool usedfor prediction and mitigation of manufacturing defects. Such simulations are predominately meant, not only to predict the onset, growth, and shape of wrinkles but also to determine the best processing condition that can yield optimized positioning of the fibers upon forming (or robot handling in the automated processes case). However, the need for use of small-time steps via explicit FE codes, facing numerical instabilities, as well as large computational time, are among notable drawbacks of the current FEtools, hindering their extensive use as fast and yet efficient digital twins in industry. This paper presents a novel woven fabric simulation technique through the application of the material point method (MPM), which enables the use of much larger time steps, facing less numerical instabilities, hence the ability to run significantly faster and efficient simulationsfor fabric materials handling and forming processes. Therefore, this method has the ability to enhance the development of automated fiber handling and preform processes by calculating the physical interactions with the MPM fiber models and rigid tool components. This enables the designers to virtually develop, test, and optimize their processes based on either algorithmicor Machine Learning applications. As a preliminary case study, forming of a hemispherical plain weave is shown, and the results are compared to theFE simulations, as well as experiments.

Keywords: material point method, woven fabric composites, forming, material handling

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Authors: Azzedine Abdedou, Khedidja Bouhadef

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The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: forced convection, porous media, oriented confined jet, fluid mechanics

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Authors: R. Bensaada, M. Almansba, M. Ould Ouali, R. Ferhoum, N. E. Hannachi

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The aim of this work is to simulate the ductile fracture of SEN specimens in aluminium alloy. The assessment of fracture toughness is performed with the calculation of Jc (the critical value of J-Integral) through the resistance curves. The study is done using finite element code calculation ABAQUSTM including an elastic plastic with damage model of material’s behaviour. The procedure involves specimens of four different thicknesses and four ligament sizes for every thickness. The material of study is an aluminium alloy 6061-T6 for which the necessary parameters to complete the study are given. We found the same results for the same specimen’s thickness and for different ligament sizes when the fracture criterion is evaluated.

Keywords: j-integral, critical-j, damage, fracture toughness

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Authors: Mohammed Belloufi, Rachid Benzine, Badreddine Sellami

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Conjugate gradient methods is useful for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical results and comparisons with other CG methods are given.

Keywords: unconstrained optimization, conjugate gradient method, strong Wolfe line search, global convergence

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Authors: Li Ziming, He Cunfu, Liu Zenghua

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With aim for delamination type defects detection in manufacturing process of seamless pipe,this paper studies the interaction of the circumferential lamb wave with delamination in aluminum pipe.The delamination is located in the middle of pipe wall.A numerical study is carried out,the circumferential lamb wave used here is CL0 mode,which is generated with a finite element method code.Wave structures from the simulation are compared with theoretical results to verify the model’s accuracy.Delamination along the circumferential direction is established by demerging nodes of the same coordinates.When CL0 mode is incident at the entrance and exit of a delamination,it generates new mode-CL1,undergoes multiple reverberation and mode conversions between the two ends of the delamination. Signals of different receptions are obtained to provide insight in using CL0 mode for locating the delamination.

Keywords: circumferential lamb wave, delamination, FEM, seamless pipe

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Authors: A. Cherifi, B. Bouazza, A. O. Dahmane, B. Yagoubi

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Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed.

Keywords: OFDM, (FrFT) fractional fourier transform, optical OFDM, equalization algorithm

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Authors: A. Mansouri, F. Krim

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This paper presents two techniques for DC motor parameters identification. We propose a numerical method using the adaptive extensive recursive least squares (AERLS) algorithm for real time parameters estimation. This algorithm, based on minimization of quadratic criterion, is realized in simulation for parameters identification of DC motor autoregressive moving average with extra inputs (ARMAX). As advanced technique, we use genetic algorithms (GA) identification with biased estimation for high dynamic performance speed regulation. DC motors are extensively used in variable speed drives, for robot and solar panel trajectory control. GA effectiveness is derived through comparison of the two approaches.

Keywords: ARMAX model, DC motor, AERLS, GA, optimization, parameter identification, PID speed regulation

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Authors: A. Chellil, A. Nour, S. Lecheb , H. Mechakra, L. Addar, H. Kebir

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This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems. Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: aluminum alloys, plate, crack, failure

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Authors: Emmanuel O. Ezim, Idowu A. Olayinka, Michael Oladunjoye, Izuchukwu I. Obiadi

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Monitoring of reservoir properties prior to well placements and production is a requirement for optimisation and efficient oil and gas production. This is usually done using well log analyses and 3-D seismic, which are often prone to errors. However, 4-D (Time-lapse) seismic, incorporating numerous 3-D seismic surveys of the same field with the same acquisition parameters, which portrays the transient changes in the reservoir due to production effects over time, could be utilised because it generates better resolution. There is, however dearth of information on the applicability of this approach in the Niger Delta. This study was therefore designed to apply 4-D seismic, well-log and geologic data in monitoring of reservoirs in the EK field of the Niger Delta. It aimed at locating bypassed accumulations and ensuring effective reservoir management. The Field (EK) covers an area of about 1200km2 belonging to the early (18ma) Miocene. Data covering two 4-D vintages acquired over a fifteen-year interval were obtained from oil companies operating in the field. The data were analysed to determine the seismic structures, horizons, Well-to-Seismic Tie (WST), and wavelets. Well, logs and production history data from fifteen selected wells were also collected from the Oil companies. Formation evaluation, petrophysical analysis and inversion alongside geological data were undertaken using Petrel, Shell-nDi, Techlog and Jason Software. Well-to-seismic tie, formation evaluation and saturation monitoring using petrophysical and geological data and software were used to find bypassed hydrocarbon prospects. The seismic vintages were interpreted, and the amounts of change in the reservoir were defined by the differences in Acoustic Impedance (AI) inversions of the base and the monitor seismic. AI rock properties were estimated from all the seismic amplitudes using controlled sparse-spike inversion. The estimated rock properties were used to produce AI maps. The structural analysis showed the dominance of NW-SE trending rollover collapsed-crest anticlines in EK with hydrocarbons trapped northwards. There were good ties in wells EK 27, 39. Analysed wavelets revealed consistent amplitude and phase for the WST; hence, a good match between the inverted impedance and the good data. Evidence of large pay thickness, ranging from 2875ms (11420 TVDSS-ft) to about 2965ms, were found around EK 39 well with good yield properties. The comparison between the base of the AI and the current monitor and the generated AI maps revealed zones of untapped hydrocarbons as well as assisted in determining fluids movement. The inverted sections through EK 27, 39 (within 3101 m - 3695 m), indicated depletion in the reservoirs. The extent of the present non-uniform gas-oil contact and oil-water contact movements were from 3554 to 3575 m. The 4-D seismic approach led to better reservoir characterization, well development and the location of deeper and bypassed hydrocarbon reservoirs.

Keywords: reservoir monitoring, 4-D seismic, well placements, petrophysical analysis, Niger delta basin

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Authors: Yang Zhong, Heng Liu

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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Ehan Sabah Shukri, Wirachman Wisnoe

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Temperature distribution investigation in a conical diffuser fitted with helical screw-tape with and without center-rod is studied numerically. A helical screw-tape is inserted in the diffuser to create swirl flow that helps to enhance the temperature distribution rate with inlet Reynolds number 4.3 x 104. Three pitch lengths ratios (Y/L = 0.153, 0.23 and 0.307) for the helical screw-tape with and without center-rod are simulated and compared. The geometry of the conical diffuser and the inlet condition for both arrangements are kept constant. Numerical findings show that the helical screw-tape inserts without center-rod perform significantly better than the helical tape inserts with center-rod in the conical diffuser.

Keywords: diffuser, temperature distribution, CFD, pitch ratio

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Authors: Maha Al-Soudani, Gilles Klysz, Jean-Paul Balayssac

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The aim of this paper is to use Ground Penetrating Radar (GPR) as a non-destructive testing (NDT) method to increase its accuracy in recognizing the geometric reinforced concrete structures and in particular, the position of steel bars. This definition will help the managers to assess the state of their structures on the one hand vis-a-vis security constraints and secondly to quantify the need for maintenance and repair. Several configurations of acquisition and processing of the simulated signal were tested to propose and develop an appropriate imaging algorithm in the propagation medium to locate accurately the rebar. A subsequent experimental validation was used by testing the imaging algorithm on real reinforced concrete structures. The results indicate that, this algorithm is capable of estimating the reinforcing steel bar position to within (0-1) mm.

Keywords: GPR, NDT, Reinforced concrete structures, Rebar location.

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Authors: N. Ourabia, M. Boubaker Ourabia

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An approach for modeling and numerical simulation of passive planar structures using the edge line concept is developed. With this method, we develop an efficient modeling technique for microstrip discontinuities. The technique obtains closed form expressions for the equivalent circuits which are used to model these discontinuities. Then, it would be easy to handle and to characterize complicated structures like T and Y junctions, truncated junctions, arbitrarily shaped junctions, cascading junctions and more generally planar multiport junctions. Another advantage of this method is that the edge line concept for arbitrary shape junctions operates with real parameters circuits. The validity of the method was further confirmed by comparing our results for various discontinuities (bend, filters) with those from HFSS as well as from other published sources.

Keywords: optimization, CAD analysis, microwave circuits, S-parameters

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Authors: Shigeyuki Haruyama, Ken Kaminishi, Junji Kaneko, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physics fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: system model, physical models, empirical models, conservation law, differential algebraic equation, object-oriented

Procedia PDF Downloads 477

Authors: D. K. Rao, M. G. M. Khan, K. G. Reddy

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The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries (OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy is skewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB is formulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: stratified sampling, optimum strata boundaries, optimum sample size, pareto distribution, mathematical programming problem, dynamic programming technique

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Authors: Liu Shengnan, Sun Liping, Zhu Jianxun

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Based on three dimensional potential flow theory and hinged rigid body motion equations, structure RAOs of Pelamis wave energy converter is analyzed. Analysis of numerical simulation is carried out on Pelamis in the irregular wave conditions, and the motion response of structures and total generated power is obtained. The paper analyzes influencing factors on the average power including diameter of floating body, section form of floating body, draft, hinged stiffness and damping. The optimum parameters are achieved in Zhejiang Province. Compared with the results of the pelamis experiment made by Glasgow University, the method applied in this paper is feasible.

Keywords: Pelamis, hinge, floating multibody, wave energy

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: M. Babul Hasan

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Management sciences (MS), big group of companies and industries or government policies (GP) is affiliated with a huge number of decision ingredients and complicated restrictions. Every factor in MS, every product in Industries or decision in GP is not always bankable in practice. After formulating these models there arises large-scale mixed integer programming (MIP) problem. In this paper, we developed decomposition-based pricing procedure to filter the unnecessary decision ingredients from MIP where the variables in huge number will be abated and the complicacy of restrictions will be elementary. A real life numerical example has been illustrated to demonstrate the methods. We develop the computer techniques for these methods by using a mathematical programming language (AMPL).

Keywords: Lagrangian relaxation, decomposition, sub-problem, master-problem, pricing, mixed IP, AMPL

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Edina Koch, Károly Gombás, Márton Maller

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The Little Plain is located along the Danube river, and this area is a “hotbed” of sand boil formation. This is due to the combination of a 100-250 m thick gravel layer beneath the Little Plain with a relatively thin blanket of poor soil spreading the gravel with variable thickness. Sand boils have a tradition and history in this area. It was possible to know which sand boil started and stopped working at what water level, and some of them even have names. The authors present a 2D finite element model of groundwater flow through a selected cross-section of the Danube river, which observed activation of piping phenomena during the 2013 flood event. Soil parametrization is based on a complex site investigation program conducted along the Danube River in the Little Plain.

Keywords: site characterization, groundwater flow, numerical modeling, sand boil

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Authors: Ikram Slamani, Hicheme Ferdjani

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This study focuses on analyzing a Griffith crack situated at the center of an infinite strip. The problem is reformulated as a hyper-singular integral equation and solved numerically using second-order Chebyshev polynomials. The primary objective is to calculate the stress intensity factor in mode 1, denoted as K1. The obtained results reveal the influence of the strip width and crack length on the stress intensity factor, assuming stress-free edges. Additionally, a comparison is made with relevant literature to validate the findings.

Keywords: center crack, Chebyshev polynomial, hyper singular integral equation, Griffith, infinite strip, stress intensity factor

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction

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Authors: Manideepa Saha, Jahnavi Chakrabarty

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Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

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Authors: Sara A. Pakvis, Giulia Scalet, Stefania Marconi, Ferdinando Auricchio, Matthijs Langelaar

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In recent developments in the field of multi-material additive manufacturing, differences in material properties are exploited to create printed shape-memory structures, which are referred to as 4D-printed structures. New printing techniques allow for the deliberate introduction of prestresses in the specimen during manufacturing, and, in combination with the right design, this enables new functionalities. This research focuses on bi-polymer 4D-printed structures, where the transformation process is based on a heat-induced glass transition in one material lowering its Young’s modulus, combined with an initial prestress in the other material. Upon the decrease in stiffness, the prestress is released, which results in the realization of an essentially pre-programmed deformation. As the design of such functional multi-material structures is crucial but far from trivial, a systematic methodology to find the design of 4D-printed structures is developed, where a finite element model is combined with a density-based topology optimization method to describe the material layout. This modeling approach is verified by a convergence analysis and validated by comparing its numerical results to analytical and published data. Specific aspects that are addressed include the interplay between the definition of the prestress and the material interpolation function used in the density-based topology description, the inclusion of a temperature-dependent stiffness relationship to simulate the glass transition effect, and the importance of the consideration of geometric nonlinearity in the finite element modeling. The efficacy of topology optimization to design 4D-printed structures is explored by applying the methodology to a variety of design problems, both in 2D and 3D settings. Bi-layer designs composed of thermoplastic polymers are printed by means of the fused deposition modeling (FDM) technology. Acrylonitrile butadiene styrene (ABS) polymer undergoes the glass transition transformation, while polyurethane (TPU) polymer is prestressed by means of the 3D-printing process itself. Tests inducing shape transformation in the printed samples through heating are performed to calibrate the prestress and validate the modeling approach by comparing the numerical results to the experimental findings. Using the experimentally obtained prestress values, more complex designs have been generated through topology optimization, and samples have been printed and tested to evaluate their performance. This study demonstrates that by combining topology optimization and 4D-printing concepts, stimuli-responsive structures with specific properties can be designed and realized.

Keywords: 4D-printing, glass transition, shape memory polymer, topology optimization

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Authors: Almaz R. Gazizov, Sergey S. Kharintsev, Myakzyum Kh. Salakhov

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This work deals with background signal suppression in tip-enhanced near-field optical microscopy (TENOM). The background appears because an optical signal is detected not only from the subwavelength area beneath the tip but also from a wider diffraction-limited area of laser’s waist that might contain another substance. The background can be reduced by using a taper probe with a grating on its lateral surface where an external illumination causes surface plasmon excitation. It requires the grating with parameters perfectly matched with a given incident light for effective light coupling. This work is devoted to an analysis of the light-grating coupling and a quest of grating parameters to enhance a near-field light beneath the tip apex. The aim of this work is to find the figure of merit of plasmon excitation depending on grating period and location of grating in respect to the apex. In our consideration the metallic grating on the lateral surface of the tapered plasmonic probe is illuminated by a plane wave, the electric field is perpendicular to the sample surface. Theoretical model of efficiency of plasmon excitation and propagation toward the apex is tested by fdtd-based numerical simulation. An electric field of the incident light is enhanced on the grating by every single slit due to lightning rod effect. Hence, grating causes amplitude and phase modulation of the incident field in various ways depending on geometry and material of grating. The phase-modulating grating on the probe is a sort of metasurface that provides manipulation by spatial frequencies of the incident field. The spatial frequency-dependent electric field is found from the angular spectrum decomposition. If one of the components satisfies the phase-matching condition then one can readily calculate the figure of merit of plasmon excitation, defined as a ratio of the intensities of the surface mode and the incident light. During propagation towards the apex, surface wave undergoes losses in probe material, radiation losses, and mode compression. There is an optimal location of the grating in respect to the apex. One finds the value by matching quadratic law of mode compression and the exponential law of light extinction. Finally, performed theoretical analysis and numerical simulations of plasmon excitation demonstrate that various surface waves can be effectively excited by using the overtones of a period of the grating or by phase modulation of the incident field. The gratings with such periods are easy to fabricate. Tapered probe with the grating effectively enhances and localizes the incident field at the sample.

Keywords: angular spectrum decomposition, efficiency, grating, surface plasmon, taper nanoantenna

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