Search results for: structural equations

Authors: Helmi Temimi

Abstract:

In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: George D. Hatzigeorgiou, Nikos G. Pnevmatikos

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This study examines the inelastic behavior of adjacent planar reinforced concrete (R.C.) frames subjected to strong ground motions. The investigation focuses on the effects of vertical ground motion on the seismic pounding. The examined structures are modeled and analyzed by RUAUMOKO dynamic nonlinear analysis program using reliable hysteretic models for both structural members and contact elements. It is found that the vertical ground motion mildly affects the seismic response of adjacent buildings subjected to structural pounding and, for this reason, it can be ignored from the displacement and interstorey drifts assessment. However, the structural damage is moderately affected by the vertical component of earthquakes.

Keywords: nonlinear seismic behavior, reinforced concrete structures, structural pounding, vertical ground motions

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Authors: H. Mahdavinezhad, M. Labbaf, H. R. Tavakoli

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In recent decades, the study and control of the destructive effects of explosive vibration in construction projects has received more attention, and several experimental equations in the field of vibration prediction as well as allowable vibration limit for various structures are presented. Researchers have developed a number of experimental equations to estimate the peak particle velocity (PPV), in which the experimental constants must be obtained at the site of the explosion by fitting the data from experimental explosions. In this study, the most important of these equations was evaluated for strong massive conglomerates around Dez Dam by collecting data on explosions, including 30 particle velocities, 27 displacements, 27 vibration frequencies and 27 acceleration of earth vibration at different distances; they were recorded in the form of two types of detonation systems, NUNEL and electric. Analysis showed that the data from the explosion had the best correlation with the cube root of the explosive, R2=0.8636, but overall the correlation coefficients are not much different. To estimate the vibration in this project, data regression was performed in the other formats, which resulted in the presentation of new equation with R2=0.904 correlation coefficient. Finally according to the importance of the studied structures in order to ensure maximum non damage to adjacent structures for each diagram, a range of application was defined so that for distances 0 to 70 meters from blast site, exponent n=0.33 and for distances more than 70 m, n =0.66 was suggested.

Keywords: blasting, blast-induced vibration, empirical equations, PPV, tunnel

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Daniel Y. Abebe, Jeonghyun Jang, Jaehyouk Choi

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This study aims to evaluate the effective size, section and structural characteristics of circular hollow steel (CHS) damper. CHS damper is among steel dampers which are used widely for seismic energy dissipation because they are easy to install, maintain and are inexpensive. CHS damper dissipates seismic energy through metallic deformation due to the geometrical elasticity of circular shape and fatigue resistance around connection part. After calculating the effective size, which is found to be height to diameter ratio of √("3"), nonlinear FE analyses were carried out to evaluate the structural characteristics and effective section (diameter-to-ratio).

Keywords: circular hollow steel damper, structural characteristics, effective size, effective section, large deformation, FE analysis

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Authors: Gleda Kutrolli, Maksi Kutrolli, Etjon Meco

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SARS-CoV-2 virus is currently one of the most infectious pathogens for humans. It started in China at the end of 2019 and now it is spread in all over the world. The origin and diffusion of the SARS-CoV-2 epidemic, is analysed based on the discussion of viral phylogeny theory. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the spread of the virus and simulate its activity. In this paper, the prediction of coronavirus outbreak is done by using SIR model without vital dynamics, applying different numerical technique solving ordinary differential equations (ODEs). We find out that ABM and MRT methods perform better than other techniques and that the activity of the virus will decrease in April but it never cease (for some time the activity will remain low) and the next cycle will start in the middle July 2020 for Norway and Denmark, and October 2020 for Sweden, and September for Finland.

Keywords: forecasting, ordinary differential equations, SARS-COV-2 epidemic, SIR model

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: Zheng Zhihao

Abstract:

Recently, Knowledge Graph Framework Network (KGCN) has developed powerful capabilities in knowledge representation and reasoning tasks. However, traditional KGCN often uses a fixed weight mechanism when aggregating information, failing to make full use of rich structural information, resulting in a certain expression ability of node representation, and easily causing over-smoothing problems. In order to solve these challenges, the paper proposes an new graph neural network model called KGCN-STAR (Knowledge Graph Convolutional Network with Structural Adaptive Receptive Fields). This model dynamically adjusts the perception of each node by introducing a structural adaptive receptive field. wild range, and a subgraph aggregator is designed to capture local structural information more effectively. Experimental results show that KGCN-STAR shows significant performance improvement on multiple knowledge graph data sets, especially showing considerable capabilities in the task of representation learning of complex structures.

Keywords: knowledge graph, graph neural networks, structural adaptive receptive fields, information aggregation

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Authors: Marinka K. Baghdasaryan, Siranush M. Muradyan, Avgen A. Gasparyan

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Analytical expressions of the current and angular errors, as well as the frequency characteristics of an induction converter describing the relation with its structural parameters, the core and winding characteristics are obtained. Based on estimation of the dependences obtained, a mathematical problem of parametric optimization is formulated which can successfully be used for investigation and diagnosing an induction converter.

Keywords: induction converters, magnetic circuit material, current and angular errors, frequency response, mathematical formulation, structural parameters

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Authors: S. Louhibi-Fasla, H. Rekab Djabri, H. Achour

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The aim of this work is to investigate the structural phase-transitions and electronic properties of copper halides. Our calculations were performed within the PLW extension to the first principle FPLMTO method, which enables an accurate treatment of all kinds of structures including the open ones. Results are given for lattice parameters, bulk modulus and its first derivatives in five different surface phases, and are compared with the available theoretical and experimental data. In the zinc-blende (B3) and PbO (B10) phases, the fundamental gap remains direct with both the top of VB and the bottom of CB located at Γ.

Keywords: FPLMTO, structural properties, Copper halides, phase transitions, ground state phase

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Authors: W. C. Bracken

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Given that concrete masonry walls are expected to experience shrinkage combined with thermal expansion and contraction, and in some cases even carbonation, throughout their service life, cracking is to be expected. However, after concrete masonry walls have been placed into service, originally anticipated and accounted for cracking is often misdiagnosed as a structural defect. Such misdiagnoses often result in or are used to support litigation. This paper begins by discussing the causes and types of anticipated cracking within concrete masonry walls followed by a discussion on the processes and analyses that exists for properly evaluating them and their significance. From here, the paper then presents a case of misdiagnosed concrete masonry cracking and the flawed logic employed to support litigation.

Keywords: concrete masonry, masonry wall cracking, structural defect, structural damage, construction defect, forensic investigation

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Authors: Richard Krijnen, Alan Wang

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As the world is aiming to reach net zero around 2050, structural engineers must begin finding solutions to contribute to this global initiative. Approximately 40% of global energy-related emissions are due to buildings and construction, and a building’s structure accounts for 50% of its embodied carbon, which indicates that structural engineers are key contributors to finding solutions to reach carbon neutrality. However, this task presents a multifaceted challenge as structural engineers must navigate technical, safety and economic considerations while striving to reduce emissions. This study reviews several options and considerations to reduce carbon emissions that structural engineers can use in their future designs without compromising the structural integrity of their proposed design. Low-carbon structures should adhere to several guiding principles. Firstly, prioritize the selection of materials with low carbon footprints, such as recyclable or alternative materials. Optimization of design and engineering methods is crucial to minimize material usage. Encouraging the use of recyclable and renewable materials reduces dependency on natural resources. Energy efficiency is another key consideration involving the design of structures to minimize energy consumption across various systems. Choosing local materials and minimizing transportation distances help in reducing carbon emissions during transport. Innovation, such as pre-fabrication and modular design or low-carbon concrete, can further cut down carbon emissions during manufacturing and construction. Collaboration among stakeholders and sharing experiences and resources are essential for advancing the development and application of low-carbon structures. This paper identifies current available tools and solutions to reduce embodied carbon in structures, which can be used as part of daily structural engineering practice.

Keywords: efficient structural design, embodied carbon, low-carbon material, sustainable structural design

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Authors: Gilbert Makanda

Abstract:

The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Phuoc Si Nguyen

Abstract:

Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: frequency transformation, bilinear z-transformation, pre-warping frequency, digital filters, analog filters, pascal’s triangle

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Authors: B. Bahloul

Abstract:

This study investigates the structural, electronic, and optical properties of LiH and NaH compounds, as well as their ternary mixed crystals LiₓNa1-ₓH, adopting a face-centered cubic structure with space group Fm-3m (number 225). The structural and electronic characteristics are examined using density functional theory (DFT), while empirical methods, specifically the modified Moss relation, are employed for analyzing optical properties. The exchange-correlation potential is determined through the generalized gradient approximation (PBEsol-GGA) within the density functional theory (DFT) framework, utilizing the projected augmented wave pseudopotentials (PAW) approach. The Quantum Espresso code is employed for conducting these calculations. The calculated lattice parameters at equilibrium volume and the bulk modulus for x=0 and x=1 exhibit good agreement with existing literature data. Additionally, the LiₓNa1-ₓH alloys are identified as having a direct band gap.

Keywords: DFT, structural, electronic, optical properties

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Authors: Takhchi Jamal, Ouisse Morvan, Sadoulet-Reboul Emeline, Bouhaddi Noureddine, Gagliardini Laurent, Bornet Frederic, Lakrad Faouzi

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Structural intensity is a technique that can be used to indicate both the magnitude and direction of power flow through a structure from the excitation source to the dissipation sink. However, current analysis is limited to the low frequency range. At medium and high frequencies, a rotational component appear in the field, masking the energy flow and make its understanding difficult or impossible. The objective of this work is to implement a methodology to filter out the rotational components of the structural intensity field in order to fully understand the energy flow in complex structures. The approach is based on the Helmholtz decomposition. It allows to decompose the structural intensity field into rotational, irrotational, and harmonic components. Only the irrotational component is needed to describe the net power flow from a source to a dissipative zone in the structure. The methodology has been applied on academic structures, and it allows a good analysis of the energy transfer paths.

Keywords: structural intensity, power flow, helmholt decomposition, irrotational intensity

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Authors: Abhilash Sahu, Amit Priyadarshi

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In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

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Authors: Alireza Taghdiri, Sara Ghanbarzade Ghomi

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Nowadays, steel structures are used for not only common buildings but also high-rise construction and wide span covering. The advanced methods of construction as well as the advanced structural connections have a great effect on architecture. However a better use of steel structural systems will be achieved with the deep understanding of steel structures specifications and their substantial advantages. On the other hand, the steel structures face to the different environmental factors such as air flow which cause erosion and corrosion. With the time passing, the amount of these steel mass damages and also the imposed stress will be increased. In other words, the position of erosion in steel structures related to existing stresses indicates that effective environmental conditions will gradually decrease the structural resistance of steel components and result in decreasing the durability of steel components. In this paper, the durability of different steel structural components is evaluated and on the basis of these stress, architectural strategies for designing the system and the components of steel structures is recognized in order to achieve an optimum life cycle.

Keywords: durability, bending stress, erosion in steel structure, life cycle

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Authors: Abdul Hakim Chikho

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Most international codes allow the use of an equivalent lateral load method for designing practical buildings to withstand earthquake actions. This method requires calculating an approximation to the fundamental mode period of vibrations of these buildings. Several empirical equations have been suggested to calculate approximations to the fundamental periods of different types of structures. Most of these equations are knowing to provide an only crude approximation to the required fundamental periods and repeating the calculation utilizing a more accurate formula is usually required. In this paper, a new formula to calculate a satisfactory approximation of the fundamental period of a practical building is proposed. This formula takes into account the mass and the stiffness of the building therefore, it is more logical than the conventional empirical equations. In order to verify the accuracy of the proposed formula, several examples have been solved. In these examples, calculating the fundamental mode periods of several farmed buildings utilizing the proposed formula and the conventional empirical equations has been accomplished. Comparing the obtained results with those obtained from a dynamic computer has shown that the proposed formula provides a more accurate estimation of the fundamental periods of practical buildings. Since the proposed method is still simple to use and requires only a minimum computing effort, it is believed to be ideally suited for design purposes.

Keywords: earthquake, fundamental mode period, design, building

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Authors: Aurore Cauquis, Philippe Heinrich, Mario Ricchiuto, Audrey Gailler

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In this talk, we look for an accurate time scheme to model the propagation of waves. Several numerical schemes have been developed to solve the extended weakly nonlinear weakly dispersive Boussinesq Equations. The temporal schemes used are two Lax-Wendroff schemes, second or third order accurate, two Runge-Kutta schemes of second and third order and a simplified third order accurate Lax-Wendroff scheme. Spatial derivatives are evaluated with fourth order accuracy. The numerical model is applied to two monodimensional benchmarks on a flat bottom. It is also applied to the simulation of the Algerian tsunami generated by a Mw=6 seism on the 18th March 2021. The tsunami propagation was highly dispersive and propagated across the Mediterranean Sea. We study here the effects of the order of temporal discretization on the accuracy of the results and on the time of computation.

Keywords: numerical analysis, tsunami propagation, water wave, boussinesq equations

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Authors: Jason Ting Jing Cheng, Lee Foo Wei, Yew Ming Kun, Mo Kim Hung, Yip Chun Chieh

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This research delves into the structural characteristics of distinct construction material, rubberized lightweight foam concrete (RLFC) wall panels, which have been developed as a sustainable alternative for the construction industry. These panels are engineered with a RLFC core, possessing a density of 1150 kg/m3, which is specifically formulated to bear structural loads. The core is enveloped with high-strength fiber cement boards, selected for their superior load-bearing capabilities, and enhanced flexural strength when compared to conventional concrete. A thin bed adhesive, known as TPS, is employed to create a robust bond between the RLFC core and the fiber cement cladding. This study underscores the potential of RLFC wall panels as a viable and eco-friendly option for modern building construction, offering a combination of structural efficiency and environmental benefits.

Keywords: structural performance, rubberized concrete wall panel, fiber cement board, insulation performance

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Authors: Ganesh Prasad Mishra, Kusum Lata Mishra

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Structural, organizational ambidexterity influences along with transformational leadership (TL) in the firms to endure viability in conditions of environmental volatility, high level of uncertainty, and possible turbulence. Combining shreds of evidence from the study of N=693 employees of a large private multi-conglomerate organization in the Middle East, we tested whether social astuteness interceded the effects of (TL) on structural, organizational ambidexterity (SOA). Other tested areas were whether status incongruence moderated transformational leadership and structural, organizational ambidexterity relationships. After analyzing through Hierarchically Linear Modelling, we found that social astuteness interceded the effects of TL on SOA, and similarly, status incongruence moderated relationships between TL and SOA. The association between TL and SOA was found to be less encouraging with a high level of status incongruence, and their relationship was strengthened by a lower level of status incongruence. We tested the hypothesized theoretical framework that articulates the conditions under which the social astuteness ideology infused in transformational leadership for achieving higher structural and organizational ambidexterity will likely occur. Findings, suggestions, and future directions for research have been deliberated in detail.

Keywords: transformational leadership, social astuteness, status incongruence, relationship, structural organizational ambidexterity.

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Authors: Ali Kezmane, Said Boukais, Mohand Hamizi

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This paper presents an analytical study on the behavior of reinforced concrete walls with rectangular cross section. Several experiments on such walls have been selected to be studied. Database from various experiments were collected and nominal shear wall strengths have been calculated using formulas, such as those of the ACI (American), NZS (New Zealand), Mexican (NTCC), and Wood and Barda equations. Subsequently, nominal shear wall strengths from the formulas were compared with the ultimate shear wall strengths from the database. These formulas vary substantially in functional form and do not account for all variables that affect the response of walls. There is substantial scatter in the predicted values of ultimate shear strength. Two new semi empirical equations are developed using data from tests of 57 walls for transitions walls and 27 for slender walls with the objective of improving the prediction of peak strength of walls with the most possible accurate.

Keywords: shear strength, reinforced concrete walls, rectangular walls, shear walls, models

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Boguslaw Schreyer

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In this paper, a general dynamical model is derived using the Lagrange formalism. The two masses: sprang and unsprang are included in a six-degree of freedom model for a sprung mass. The unsprung mass is included and shown only in a simplified model, although its equations have also been derived by an author. The simplified equations, more suitable for the computer model of robot’s dynamics are also shown.

Keywords: dynamics, mobile, robot, wheeled mobile robots

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Authors: Joanna Pietrzak, Anna Stefanska, Wieslaw Rokicki

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Contemporary high-rise buildings constructed in recent years are often tremendous examples of original and unique architectural forms, being at the same time the affirmation of technical and technological progress accomplishments. The search for more efficient, sophisticated generations of structures also concerns the shaping of high-quality details. The concept of structural detail designing is connected with the rationalization of engineering solutions as well as through the optimisation and reduction of used material. Contemporary structural detail perceived through the development of building technologies is often a very aesthetic technical and material solution, which significantly influences the visual perception of architecture. Structural details are more often seen in shaping the forms of high-rise buildings, which are erected in many culturally different countries.

Keywords: aesthetic expression, high-rise buildings, structural detail, tall buildings

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Authors: Keltoum Bouherine, Olivier Leroy

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The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.The present work is dedicated to study a three–dimensional (3D) self-consistent fluid simulation of microwave discharges of argon plasma in PECVD reactor. The model solves the Maxwell’s equations, continuity equations for charged species and the electron energy balance equation, coupled with Poisson’s equation, and Navier-Stokes equations by finite element method, using COMSOL Multiphysics software. In this study, the simulations yield the profiles of plasma components as well as the charge densities and electron temperature, the electric field, the gas velocity, and gas temperature. The results show that the microwave plasma reactor is outside of local thermodynamic equilibrium.

Keywords: electron density, electric field, microwave plasma reactor, gas velocity, non-equilibrium plasma

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Authors: M. H. Kazemi, D. Salac

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A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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