Search results for: nonlinear optics

Authors: Teng Li, Kamran Mohseni

Abstract:

This paper presents an inviscid regularization technique that is capable of regularizing the shocks and sharp interfaces simultaneously in the shock-interface interaction simulations. The direct numerical simulation of flows involving shocks has been investigated for many years and a lot of numerical methods were developed to capture the shocks. However, most of these methods rely on the numerical dissipation to regularize the shocks. Moreover, in high Reynolds number flows, the nonlinear terms in hyperbolic Partial Differential Equations (PDE) dominates, constantly generating small scale features. This makes direct numerical simulation of shocks even harder. The same difficulty happens in two-phase flow with sharp interfaces where the nonlinear terms in the governing equations keep sharpening the interfaces to discontinuities. The main idea of the proposed technique is to average out the small scales that is below the resolution (observable scale) of the computational grid by filtering the convective velocity in the nonlinear terms in the governing PDE. This technique is named “observable method” and it results in a set of hyperbolic equations called observable equations, namely, observable Navier-Stokes or Euler equations. The observable method has been applied to the flow simulations involving shocks, turbulence, and two-phase flows, and the results are promising. In the current paper, the observable method is examined on the performance of regularizing shocks and interfaces at the same time in shock-interface interaction problems. Bubble-shock interactions and Richtmyer-Meshkov instability are particularly chosen to be studied. Observable Euler equations will be numerically solved with pseudo-spectral discretization in space and third order Total Variation Diminishing (TVD) Runge Kutta method in time. Results are presented and compared with existing publications. The interface acceleration and deformation and shock reflection are particularly examined.

Keywords: compressible flow simulation, inviscid regularization, Richtmyer-Meshkov instability, shock-bubble interactions.

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Authors: Paffrath Meinhard, Zhou Yayun, Guo Yiqing, Ertl Harald

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Winding geometry design is an important part of power transformer electrical design. Conventionally, the winding geometry is designed manually, which is a time-consuming job because it involves many iteration steps in order to meet all cost, manufacturing and electrical requirements. Here a method is presented which automatically generates the winding geometry for given user parameters and allows the user to interactively set and change parameters. To achieve this goal, the winding problem is transferred to a mixed integer nonlinear optimization problem. The relevant geometrical design parameters are defined as optimization variables. The cost and other requirements are modeled as constraints. For the solution, a stochastic ant colony optimization algorithm is applied. It is well-known, that an optimizer can get stuck in a local minimum. For the winding problem, we present efficient strategies to come out of local minima, furthermore a reduced variable search range helps to accelerate the solution process. Numerical examples show that the optimization result is delivered within seconds such that the user can interactively change the variable search area and constraints to improve the design.

Keywords: ant colony optimization, mixed integer nonlinear programming, power transformer, winding design

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Authors: Mostafa Jafarian Abyaneh, Khashayar Jafari, Vahab Toufigh

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The cost of experiments on different types of concrete has raised the demand for prediction of their behavior with numerical analysis. In this research, an advanced numerical model has been presented to predict the complete elastic-plastic behavior of polymer concrete (PC), high-strength concrete (HSC), high performance concrete (HPC) along with different steel fiber contents under uniaxial compression. The accuracy of the numerical response was satisfactory as compared to other conventional simple models such as Mohr-Coulomb and Drucker-Prager. In order to predict the complete elastic-plastic behavior of specimens including softening behavior, disturbed state concept (DSC) was implemented by nonlinear finite element analysis (NFEA) and hierarchical single surface (HISS) failure criterion, which is a failure surface without any singularity.

Keywords: disturbed state concept (DSC), hierarchical single surface (HISS) failure criterion, high performance concrete (HPC), high-strength concrete (HSC), nonlinear finite element analysis (NFEA), polymer concrete (PC), steel fibers, uniaxial compression test

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Authors: N. Ould cherchali, M. S. Boucherit, L. Barazane, A. Morsli

Abstract:

Photovoltaic power is widely used to supply isolated or unpopulated areas (lighting, pumping, etc.). Great advantage is that this source is inexhaustible, it offers great safety in use and it is clean. But the dynamic models used to describe a photovoltaic system are complicated and nonlinear and due to nonlinear I-V and P–V characteristics of photovoltaic generators, a maximum power point tracking technique (MPPT) is required to maximize the output power. In this paper, two online techniques of maximum power point tracking using robust controller for photovoltaic systems are proposed, the first technique use fuzzy logic controller (FLC) and the second use sliding mode controller (SMC) for photovoltaic systems. The two maximum power point tracking controllers receive the partial derivative of power as inputs, and the output is the duty cycle corresponding to maximum power. A Photovoltaic generator with Boost converter is developed using MATLAB/Simulink to verify the preferences of the proposed techniques. SMC technique provides a good tracking speed in fast changing irradiation and when the irradiation changes slowly or is constant the panel power of FLC technique presents a much smoother signal with less fluctuations.

Keywords: fuzzy logic controller, maximum power point, photovoltaic system, tracker, sliding mode controller

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Authors: David Kriebel, Jan Edgar Mehner

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The paper introduces a method to efficiently simulate nonlinear changing electrostatic fields occurring in micro-electromechanical systems (MEMS). Large deflections of the capacitor electrodes usually introduce nonlinear electromechanical forces on the mechanical system. Traditional finite element methods require a time-consuming remeshing process to capture exact results for this physical domain interaction. In order to accelerate the simulation process and eliminate the remeshing process, a formulation of a strongly coupled electromechanical transducer element will be introduced, which uses a combination of finite-element with an advanced mesh morphing technique using radial basis functions (RBF). The RBF allows large geometrical changes of the electric field domain while retaining the high element quality of the deformed mesh. Coupling effects between mechanical and electrical domains are directly included within the element formulation. Fringing field effects are described accurately by using traditional arbitrary shape functions.

Keywords: electromechanical, electric field, transducer, simulation, modeling, finite-element, mesh morphing, radial basis function

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Authors: Aran Dezhban, Hooshang Dolatshahi Pirooz

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The phenomenon of corrosion, especially in the Persian Gulf region, is the main cause of the deterioration of offshore platforms, due to the high corrosion of its water. This phenomenon occurs mostly in the area of water spraying, threatening the members of the first floor of the jacket, legs, and piles in this area. In the current study, the effect of bracing arrangement on the Capacity Curve and Reserve Strength Ratio of Fixed-Type Offshore Platforms is investigated. In order to continue the operation of the platform, two modes of robust and damaged structures are considered, while checking the adequacy of the platform capacity based on the allowable values of API RP-2SIM regulations. The platform in question is located in the Persian Gulf, which is modeled on the OpenSEES software. In this research, the Nonlinear Pushover Analysis has been used. After validation, the Capacity Curve of the studied platforms is obtained and then their Reserve Strength Ratio is calculated. Results are compared with the criteria in the API-2SIM regulations.

Keywords: fixed-type jacket structure, structural integrity management, nonlinear pushover analysis, robust and damaged structure, reserve strength ration, capacity curve

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Authors: Emre Akyürek, Anthony Huynh, Tatiana Kalganova

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The Ambidextrous Robot Hand is a robotic device with the purpose to mimic either the gestures of a right or a left hand. The symmetrical behavior of its fingers allows them to bend in one way or another keeping a compliant and anthropomorphic shape. However, in addition to gestures they can reproduce on both sides, an asymmetrical mechanical design with a three tendons routing has been engineered to reduce the number of actuators. As a consequence, control algorithms must be adapted to drive efficiently the ambidextrous fingers from one position to another and to include grasping features. These movements are controlled by pneumatic muscles, which are nonlinear actuators. As their elasticity constantly varies when they are under actuation, the length of pneumatic muscles and the force they provide may differ for a same value of pressurized air. The control algorithms introduced in this paper take both the fingers asymmetrical design and the pneumatic muscles nonlinearity into account to permit an accurate control of the Ambidextrous Robot Hand. The finger motion is achieved by combining a classic PID controller with a phase plane switching control that turns the gain constants into dynamic values. The grasping ability is made possible because of a sliding mode control that makes the fingers adapt to the shape of an object before strengthening their positions.

Keywords: ambidextrous hand, intelligent algorithms, nonlinear actuators, pneumatic muscles, robotics, sliding control

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Authors: H. Bonakdari, I. Ebtehaj

Abstract:

The prediction of scour depth around bridge piers is frequently considered in river engineering. One of the key aspects in efficient and optimum bridge structure design is considered to be scour depth estimation around bridge piers. In this study, scour depth around bridge piers is estimated using two methods, namely the Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN). Therefore, the effective parameters in scour depth prediction are determined using the ANN and ANFIS methods via dimensional analysis, and subsequently, the parameters are predicted. In the current study, the methods’ performances are compared with the nonlinear regression (NLR) method. The results show that both methods presented in this study outperform existing methods. Moreover, using the ratio of pier length to flow depth, ratio of median diameter of particles to flow depth, ratio of pier width to flow depth, the Froude number and standard deviation of bed grain size parameters leads to optimal performance in scour depth estimation.

Keywords: adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), bridge pier, scour depth, nonlinear regression (NLR)

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Authors: Abdelmalek Ouannou, Adil Brouri, Laila Kadi, Tarik

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Switched reluctance motor (SRM) has a major interest in a large domain as in electric vehicle driving because of its wide range of speed operation, high performances, low cost, and robustness to run under degraded conditions. The purpose of the paper is to develop a new analytical approach for modeling SRM parameters. Then, an identification scheme is proposed to obtain the SRM parameters. Since the SRM is featured by a highly nonlinear behavior, modeling these devices is difficult. Then, it is convenient to develop an accurate model describing the SRM. Furthermore, it is always operated in the magnetically saturated mode to maximize the energy transfer. Accordingly, it is shown that the SRM can be accurately described by a generalized polynomial Hammerstein model, i.e., the parallel connection of several Hammerstein models having polynomial nonlinearity. Presently an analytical identification method is developed using a chirp excitation signal. Afterward, the parameters of the obtained model have been determined using Finite Element Method analysis. Finally, in order to show the effectiveness of the proposed method, a comparison between the true and estimate models has been performed. The obtained results show that the output responses are very close.

Keywords: switched reluctance motor, swept-sine signal, generalized Hammerstein model, nonlinear system

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Authors: H. Hotait, X. Chiementin, L. Rasolofondraibe

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This paper presents a continuous work to detect the abnormal state in the rolling bearing by studying the vibration signature analysis and calculation of the remaining useful life. To achieve these aims, two methods; the first method is the classification to detect the degradation state by the AOM-OPTICS (Acousto-Optic Modulator) method. The second one is the prediction of the degradation state using least-squares support vector regression and then compared with the linear degradation model. An experimental investigation on ball-bearing was conducted to see the effectiveness of the used method by applying the acquired vibration signals. The proposed model for predicting the state of bearing gives us accurate results with the experimental and numerical data.

Keywords: bearings, automatization, optimization, prognosis, classification, defect detection

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Authors: Shank Kulkarni, Alireza Tabarraei

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The fantastic properties of polyurea such as flexibility, durability, and chemical resistance have brought it a wide range of application in various industries. Effective prediction of the response of polyurea under different loading and environmental conditions necessitates the development of an accurate constitutive model. Similar to most polymers, the behavior of polyurea depends on both strain and strain rate. Therefore, the constitutive model should be able to capture both these effects on the response of polyurea. To achieve this objective, in this paper, a nonlinear hyper-viscoelastic constitutive model is developed by the superposition of a hyperelastic and a viscoelastic model. The proposed constitutive model can capture the behavior of polyurea under compressive loading conditions at various strain rates. Four parameter Ogden model and Mooney Rivlin model are used to modeling the hyperelastic behavior of polyurea. The viscoelastic behavior is modeled using both a three-parameter standard linear solid (SLS) model and a K-BKZ model. Comparison of the modeling results with experiments shows that Odgen and SLS model can more accurately predict the behavior of polyurea. The material parameters of the model are found by curve fitting of the proposed model to the uniaxial compression test data. The proposed model can closely reproduce the stress-strain behavior of polyurea for strain rates up to 6500 /s.

Keywords: constitutive modelling, ogden model, polyurea, SLS model, uniaxial compression test

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Authors: Mao Li, Yuguang Ma, Katsuhiko Ariga

Abstract:

The performance of functional materials is governed by their ability to interact with surrounding environments in a well-defined and controlled manner. Layer-by-Layer (LbL) assembly is one of the most widely used technologies for coating both planar and particulate substrates in a diverse range of fields, including optics, energy, catalysis, separations, and biomedicine. Herein, we introduce electrochemical-coupling layer-by-layer assembly as a novel fabrication methodology for preparing layered thin films. This assembly method not only determines the process properties (such as the time, scalability, and manual intervention) but also directly control the physicochemical properties of the films (such as the thickness, homogeneity, and inter- and intra-layer film organization), with both sets of properties linked to application-specific performance.

Keywords: layer by layer assembly, electropolymerization, carbazole, optical thin film, electronics

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Authors: Mohsen Tehranizadeh, Mahboobe Forghani

Abstract:

The impact of higher modes on the seismic response of dual structural system consist of concrete moment-resisting frame and with RC shear walls is investigated against near-field earthquakes in this paper. a 20 stories reinforced concrete shear wall-special moment frame structure is designed in accordance with ASCE7 requirements and The nonlinear model of the structure was performed on OpenSees platform. Nonlinear time history dynamic analysis with 3 near-field records are performed on them. In order to further understand the structural collapse behavior in the near field, the response of the structure at the moment of collapse especially the formation of plastic hinges is explored. The results revealed that the amplification of moment at top of the wall due to higher modes, the plastic hinge can form in the upper part of wall, even when designed and detailed for plastic hinging at the base only (according to ACI code).on the other hand, shear forces in excess of capacity design values can develop due to the contribution of the higher modes of vibration to dynamic response due to the near field can cause brittle shear or sliding failure modes. The past investigation on shear walls clearly shows the dual-hinge design concept is effective at reducing the effects of the second mode of response. An advantage of the concept is that, when combined with capacity design, it can result in relaxation of special reinforcing detailing in large portions of the wall. In this study, to investigate the implications of multi-design approach, 4 models with varies arrangement of hinge plastics at the base and height of the shear wall are considered. results base on time history analysis showed that the dual or multi plastic hinges approach can be useful in order to control the high moment and shear demand of higher mode effect.

Keywords: higher mode effect, Near-field earthquake, nonlinear time history analysis, multi plastic hinge design

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Authors: Darius Diogo Barreto, Ajeet Kumar, Sushma Santapuri

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We present an axisymmetric variational formulation for coupled extension-torsion-inflation deformation in magnetoelastomeric thin tubes when both azimuthal and axial magnetic fields are applied. The tube's material is assumed to have a preferred magnetization direction which imparts helical magnetic anisotropy to the tube. We have also derived the expressions of the first derivative of free energy per unit tube's undeformed length with respect to various imposed strain parameters. On applying the thin tube limit, the two nonlinear ordinary differential equations to obtain the in-plane radial displacement and radial component of the Lagrangian magnetic field get converted into a set of three simple algebraic equations. This allows us to obtain simple analytical expressions in terms of the applied magnetic field, magnetization direction, and magnetoelastic constants, which tell us how these parameters can be tuned to generate positive/negative Poisson's effect in such tubes. We consider both torsionally constrained and torsionally relaxed stretching of the tube. The study can be useful in designing magnetoelastic tubular actuators.

Keywords: nonlinear magnetoelasticity, extension-torsion coupling, negative Poisson's effect, helical anisotropy, thin tube

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Authors: Andreas Rudisch, Ralf Lampert, Andreas Kolbitsch

Abstract:

It is a well-known fact among the engineering community that earthquakes with comparatively low magnitudes can cause serious damage to nonstructural components (NSCs) of buildings, even when the supporting structure performs relatively well. Past research works focused mainly on NSCs of nuclear power plants and industrial plants. Particular attention should also be given to architectural façade elements of old masonry buildings (e.g. ornamental figures, balustrades, vases), which are very vulnerable under seismic excitation. Large numbers of these historical nonstructural components (HiNSCs) can be found in highly frequented historical city centers and in the event of failure, they pose a significant danger to persons. In order to estimate the vulnerability of acceleration sensitive HiNSCs, the peak horizontal floor acceleration (PHFA) is used. The PHFA depends on the dynamic characteristics of the building, the ground excitation, and induced nonlinearities. Consequently, the PHFA can not be generalized as a simple function of height. In the present research work, an extensive case study was conducted to investigate the influence of induced nonlinearity on the PHFA for old masonry buildings. Probabilistic nonlinear FE time-history analyses considering three different hazard levels were performed. A set of eighteen synthetically generated ground motions was used as input to the structure models. An elastoplastic macro-model (multiPlas) for nonlinear homogenized continuum FE-calculation was calibrated to multiple scales and applied, taking specific failure mechanisms of masonry into account. The macro-model was calibrated according to the results of specific laboratory and cyclic in situ shear tests. The nonlinear macro-model is based on the concept of multi-surface rate-independent plasticity. Material damage or crack formation are detected by reducing the initial strength after failure due to shear or tensile stress. As a result, shear forces can only be transmitted to a limited extent by friction when the cracking begins. The tensile strength is reduced to zero. The first goal of the calibration was the consistency of the load-displacement curves between experiment and simulation. The calibrated macro-model matches well with regard to the initial stiffness and the maximum horizontal load. Another goal was the correct reproduction of the observed crack image and the plastic strain activities. Again the macro-model proved to work well in this case and shows very good correlation. The results of the case study show that there is significant scatter in the absolute distribution of the PHFA between the applied ground excitations. An absolute distribution along the normalized building height was determined in the framework of probability theory. It can be observed that the extent of nonlinear behavior varies for the three hazard levels. Due to the detailed scope of the present research work, a robust comparison with code-recommendations and simplified PHFA distributions are possible. The chosen methodology offers a chance to determine the distribution of PHFA along the building height of old masonry structures. This permits a proper hazard assessment of HiNSCs under seismic loads.

Keywords: nonlinear macro-model, nonstructural components, time-history analysis, unreinforced masonry

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Authors: H. Meddah, M. Berediaf-Bourahla, B. El-Djouzi, N. Bourahla

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Shear walls made of cold formed steel are used as lateral force resisting components in residential and low-rise commercial and industrial constructions. The seismic design analysis of such structures is often complex due to the slenderness of members and their instability prevalence. In this context, a simplified modeling technique across the panel is proposed by using the finite element method. The approach is based on idealizing the whole panel by a nonlinear shear link element which reflects its shear behavior connected to rigid body elements which transmit the forces to the end elements (studs) that resist the tension and the compression. The numerical model of the shear wall panel was subjected to cyclic loads in order to evaluate the seismic performance of the structure in terms of lateral displacement and energy dissipation capacity. In order to validate this model, the numerical results were compared with those from literature tests. This modeling technique is particularly useful for the design of cold formed steel structures where the shear forces in each panel and the axial forces in the studs can be obtained using spectrum analysis.

Keywords: cold-formed steel, cyclic loading, modeling technique, nonlinear analysis, shear wall panel

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Authors: H. Bensouilah, H. Boucherit, M. Lahmar

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A theoretical investigation on the effects of both steady-state and dynamic deformations of the foils on the dynamic performance characteristics of a self-acting air foil journal bearing operating under small harmonic vibrations is proposed. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkins’ finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the nonlinear transient compressible Reynolds’ equation. The stiffness of a bump is uniformly distributed throughout the bearing surface (generation I bearing). It was found that the dynamic properties of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

Keywords: elasto-aerodynamic lubrication, air foil bearing, steady-state deformation, dynamic deformation, stiffness and damping coefficients, perturbation method, fluid-structure interaction, Galerk infinite element method, finite difference method

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Authors: André Lages, Victor Dmitriev, Juliano Bazzo, Gianni Portela

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This work evaluates the feasibility of the graphene application to perform as a wideband reconfigurable material for lens antennas in 5G/6G and satellite applications. Based on transformation optics principles, the electromagnetic waves can be efficiently guided by modifying the effective refractive index. Graphene behavior can range between a lossy dielectric and a good conductor due to the variation of its chemical potential bias, thus arising as a promising solution for electromagnetic devices. The graphene properties and a lens antenna comprising multiples layers and periodic arrangements of graphene patches were analyzed using full-wave simulations. A dipole directivity was improved from 7 to 18.5 dBi at 29 GHz. In addition, the realized gain was enhanced 7 dB across a 14 GHz bandwidth within the Ka/5G band.

Keywords: 5G/6G, graphene, lens, reconfigurable, satellite

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Authors: Djamel Ouzandja, Boualem Tiliouine

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The safety evaluation of the concrete gravity dams subjected to seismic excitations is really very complex as the earthquake response of the concrete gravity dam depends upon its contraction joints with foundation soil. This paper presents the seismic response of concrete gravity dams considering friction contact and welded contact. Friction contact is provided using contact elements. Two-dimensional (2D) finite element model of Oued Fodda concrete gravity dam, located in Chlef at the west of Algeria, is used for this purpose. Linear and nonlinear analyses considering dam-foundation soil interaction are performed using ANSYS software. The reservoir water is modeled as added mass using the Westergaard approach. The Drucker-Prager model is preferred for dam and foundation rock in nonlinear analyses. The surface-to-surface contact elements based on the Coulomb's friction law are used to describe the friction. These contact elements use a target surface and a contact surface to form a contact pair. According to this study, the seismic analysis of concrete gravity dams including base sliding. When the friction contact is considered in joints, the base sliding displacement occurs along the dam-foundation soil contact interface. Besides, the base sliding may generally decrease the principal stresses in the dam.

Keywords: concrete gravity dam, dynamic soil-structure interaction, friction contact, sliding

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Authors: Abid Ali Abid

Abstract:

One-dimensional (1-D) particle-in-cell (PIC) electrostatic simulations are carried out to investigate the electrostatic waves, whose constituents are hot, cold and beam electrons in the background of motionless positive ions. In fact, the electrostatic modes excited are electron acoustic waves, beam driven waves as well as Langmuir waves. It is assessed that the relevant plasma parameters, for example, hot electron temperature, beam electron drift speed, and the electron beam density significantly modify the electrostatics wave's profiles. In the nonlinear stage, the wave-particle interaction becomes more evident and the waves have obtained its saturation level. Consequently, electrons become trapped in the waves and trapping vortices are clearly formed. Because of this trapping vortices and mixing of the electrons in phase space, finally, lead to electrons thermalization. It is observed that for the high-density value of the beam-electron, the solitary waves having a bipolar form of the electric field. These solitons are the nonlinear Brenstein-Greene and Kruskal wave mode that attributes the trapping of electrons potential well of phase-space hole. These examinations revealed that electrostatic waves have been exited in beam-plasma model and producing waves having broad-frequency ranges, which may clarify the broadband electrostatic noise (BEN) spectrum studied in the auroral zone.

Keywords: electron acoustic waves, trapping of cold electron, Langmuir waves, particle-in cell simulation

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Authors: F. Sangiorgio, J. Silfwerbrand, G. Mancini

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Geometric and mechanical properties all influence the resistance of RC structures and may, in certain combination of property values, increase the risk of a brittle failure of the whole system. This paper presents a statistical and probabilistic investigation on the resistance of RC beams designed according to Eurocodes 2 and 8, and subjected to multiple failure modes, under both the natural variation of material properties and the uncertainty associated with cross-section and transverse reinforcement geometry. A full probabilistic model based on JCSS Probabilistic Model Code is derived. Different beams are studied through material nonlinear analysis via Monte Carlo simulations. The resistance model is consistent with Eurocode 2. Both a multivariate statistical evaluation and the data clustering analysis of outcomes are then performed. Results show that the ultimate load behaviour of RC beams subjected to flexural and shear failure modes seems to be mainly influenced by the combination of the mechanical properties of both longitudinal reinforcement and stirrups, and the tensile strength of concrete, of which the latter appears to affect the overall response of the system in a nonlinear way. The model uncertainty of the resistance model used in the analysis plays undoubtedly an important role in interpreting results.

Keywords: modelling, Monte Carlo simulations, probabilistic models, data clustering, reinforced concrete members, structural design

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Authors: Seyedehsomayeh Hosseini

Abstract:

Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

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Authors: N. F. Hanna, A. M. Haridy

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One of the main drawbacks of the Modal Pushover Analysis (MPA) is the need to perform nonlinear time-history analysis, which complicates the analysis method and time. A simplified version of the MPA has been proposed based on the concept of the inelastic deformation ratio. Furthermore, the effect of the higher modes of vibration is considered by assuming linearly-elastic responses, which enables the use of standard elastic response spectrum analysis. In this thesis, the simplified MPA (SMPA) method is applied to determine the target global drift and the inter-story drifts of steel frame building. The effect of the higher vibration modes is considered within the framework of the SMPA. A comprehensive survey about the inelastic deformation ratio is presented. After that, a suitable expression from literature is selected for the inelastic deformation ratio and then implemented in the SMPA. The estimated seismic demands using the SMPA, such as target drift, base shear, and the inter-story drifts, are compared with the seismic responses determined by applying the standard MPA. The accuracy of the estimated seismic demands is validated by comparing with the results obtained by the nonlinear time-history analysis using real earthquake records.

Keywords: modal analysis, pushover analysis, seismic performance, target displacement

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Authors: Swati Sharma, R. P. Sharma

Abstract:

We intend to study the nonlinear evolution of the parallel propagating finite frequency Alfvén wave (also called Dispersive Alfvén wave/Hall MHD wave) propagating in the solar wind regime of the solar region when a perpendicularly propagating magnetosonic wave is present in the background. The finite frequency Alfvén wave behaves differently from the usual non-dispersive behavior of the Alfvén wave. To study the nonlinear processes (such as filamentation) taking place in the solar regions such as solar wind, the dynamical equation of both the waves are derived. Numerical simulation involving finite difference method for the time domain and pseudo spectral method for the spatial domain is then performed to analyze the transient evolution of these waves. The power spectra of the Dispersive Alfvén wave is also investigated. The power spectra shows the distribution of the magnetic field intensity of the Dispersive Alfvén wave over different wave numbers. For DAW the spectra shows a steepening for scales larger than the proton inertial length. This means that the wave energy gets transferred to the solar wind particles as the wave reaches higher wave numbers. This steepening of the power spectra can be explained on account of the finite frequency of the Alfvén wave. The obtained results are consistent with the observations made by CLUSTER spacecraft.

Keywords: solar wind, turbulence, dispersive alfven wave

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Authors: Amin Noor, Roslinda Nazar, Norihan Md. Arifin

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In this paper, a numerical and theoretical study has been performed for the stagnation-point boundary layer flow and heat transfer towards a shrinking sheet in a nanofluid. The mathematical nanofluid model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Numerical results are obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction Φ, the shrinking parameter λ and the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that solutions do not exist for larger shrinking rates and dual (upper and lower branch) solutions exist when λ < -1.0. A stability analysis has been performed to show which branch solutions are stable and physically realizable. It is also found that the upper branch solutions are stable while the lower branch solutions are unstable.

Keywords: heat transfer, nanofluid, shrinking sheet, stability analysis, stagnation-point flow

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Authors: Eloise C. Tredenick, Troy W. Farrell, W. Alison Forster, Steven T. P. Psaltis

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The agriculture industry requires improved efficacy of sprays being applied to crops. More efficacious sprays provide many environmental and financial benefits. The plant leaf cuticle is known to be the main barrier to diffusion of agrochemicals within the leaf. The importance of a mathematical model to simulate uptake of agrochemicals in plant cuticles has been noted, as the results of each uptake experiments are specific to each formulation of active ingredient and plant species. In this work we develop a mathematical model and numerical simulation for the uptake of ionic agrochemicals through aqueous pores in plant cuticles. We propose a nonlinear porous diffusion model of ionic agrochemicals in isolated cuticles, which provides additions to a simple diffusion model through the incorporation of parameters capable of simulating plant species' variations, evaporation of surface droplet solutions and swelling of the aqueous pores with water. The model could feasibly be adapted to other ionic active ingredients diffusing through other plant species' cuticles. We validate our theoretical results against appropriate experimental data, discuss the key sensitivities in the model and relate theoretical predictions to appropriate physical mechanisms.

Keywords: aqueous pores, ionic active ingredient, mathematical model, plant cuticle, porous diffusion

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Authors: Woo Young Jung, Min Ho Kwon, Bu Seog Ju

Abstract:

A failure of the non-structural component can cause significant damages in critical facilities such as nuclear power plants and hospitals. Historically, it was reported that the damage from the leakage of sprinkler systems, resulted in the shutdown of hospitals for several weeks by the 1971 San Fernando and 1994 North Ridge earthquakes. In most cases, water leakages were observed at the cross joints, sprinkler heads, and T-joint connections in piping systems during and after the seismic events. Hence, the primary objective of this study was to understand the seismic performance of T-joint connections and to develop an analytical Finite Element (FE) model for the T-joint systems of 2-inch fire protection piping system in hospitals subjected to seismic ground motions. In order to evaluate the FE models of the piping systems using OpenSees, two types of materials were used: 1) Steel 02 materials and 2) Pinching 4 materials. Results of the current study revealed that the nonlinear moment-rotation FE models for the threaded T-joint reconciled well with the experimental results in both FE material models. However, the system-level fragility determined from multiple nonlinear time history analyses at the threaded T-joint was slightly different. The system-level fragility at the T-joint, determined by Pinching 4 material was more conservative than that of using Steel 02 material in the piping system.

Keywords: fragility, t-joint, piping, leakage, sprinkler

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Authors: Charly Julien Nyobe, Eric Jacquelin, Denis Brizard, Alexy Mercier

Abstract:

The performance of road side safety barriers depends largely on the dynamic interactions between post and soil. These interactions play a key role in the response of barriers to crash testing. In the literature, soil-post interaction is modeled in crash test simulations using three approaches. Many researchers have initially used the finite element approach, in which the post is embedded in a continuum soil modelled by solid finite elements. This method represents a more comprehensive and detailed approach, employing a mesh-based continuum to model the soil’s behavior and its interaction with the post. Although this method takes all soil properties into account, it is nevertheless very costly in terms of simulation time. In the second approach, all the points of the post located at a predefined depth are fixed. Although this approach reduces CPU computing time, it overestimates soil-post stiffness. The third approach involves modeling the post as a beam supported by a set of nonlinear springs in the horizontal directions. For support in the vertical direction, the posts were constrained at a node at ground level. This approach is less costly, but the literature does not provide a simple procedure to determine the constitutive law of the springs The aim of this study is to propose a simple and low-cost procedure to obtain the constitutive law of nonlinear springs that model the soil-post interaction. To achieve this objective, we will first present a procedure to obtain the constitutive law of nonlinear springs thanks to the simulation of a soil compression test. The test consists in compressing the soil contained in the tank by a rigid solid, up to a vertical displacement of 200 mm. The resultant force exerted by the ground on the rigid solid and its vertical displacement are extracted and, a force-displacement curve was determined. The proposed procedure for replacing the soil with springs must be tested against a reference model. The reference model consists of a wooden post embedded into the ground and impacted with an impactor. Two simplified models with springs are studied. In the first model, called Kh-Kv model, the springs are attached to the post in the horizontal and vertical directions. The second Kh model is the one described in the literature. The two simplified models are compared with the reference model according to several criteria: the displacement of a node located at the top of the post in vertical and horizontal directions; displacement of the post's center of rotation and impactor velocity. The results given by both simplified models are very close to the reference model results. It is noticeable that the Kh-Kv model is slightly better than the Kh model. Further, the former model is more interesting than the latter as it involves less arbitrary conditions. The simplified models also reduce the simulation time by a factor 4. The Kh-Kv model can therefore be used as a reliable tool to represent the soil-post interaction in a future research and development of road safety barriers.

Keywords: crash tests, nonlinear springs, soil-post interaction modeling, constitutive law

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Authors: S. Behnia, S. Fathizadeh, A. Akhshani

Abstract:

In the recent decades, DNA has increasingly interested in the potential technological applications that not directly related to the coding for functional proteins that is the expressed in form of genetic information. One of the most interesting applications of DNA is related to the construction of nanostructures of high complexity, design of functional nanostructures in nanoelectronical devices, nanosensors and nanocercuits. In this field, DNA is of fundamental interest to the development of DNA-based molecular technologies, as it possesses ideal structural and molecular recognition properties for use in self-assembling nanodevices with a definite molecular architecture. Also, the robust, one-dimensional flexible structure of DNA can be used to design electronic devices, serving as a wire, transistor switch, or rectifier depending on its electronic properties. In order to understand the mechanism of the charge transport along DNA sequences, numerous studies have been carried out. In this regard, conductivity properties of DNA molecule could be investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model. In SSH model, the non-diagonal matrix element dependence on intersite displacements is considered. In this approach, the coupling between the charge and lattice deformation is along the helix. This model is a tight-binding linear nanoscale chain established to describe conductivity phenomena in doped polyethylene. It is based on the assumption of a classical harmonic interaction between sites, which is linearly coupled to a tight-binding Hamiltonian. In this work, the Hamiltonian and corresponding motion equations are nonlinear and have high sensitivity to initial conditions. Then, we have tried to move toward the nonlinear dynamics and phase space analysis. Nonlinear dynamics and chaos theory, regardless of any approximation, could open new horizons to understand the conductivity mechanism in DNA. For a detailed study, we have tried to study the current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram.

Keywords: DNA conductivity, Landauer resistance, negative dierential resistance, Chaos theory, mean Lyapunov exponent

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Authors: M. Kowalik, J. Masternak, K. Kazimierczuk, O. V. Khavryuchenko, B. Kupcewicz, B. Barszcz

Abstract:

Recently, the growing interest of chemists in metal-organic coordination polymers (MOCPs) is primarily derived from their intriguing structures and potential applications in catalysis, gas storage, molecular sensing, ion exchanges, nonlinear optics, luminescence, etc. Currently, we are devoting considerable effort to finding the proper method of synthesizing new coordination polymers containing S- or N-heteroaromatic carboxylates as linkers and characterizing the obtained Pb(II) compounds according to their structural diversity, luminescence, and thermal properties. The choice of Pb(II) as the central ion of MOCPs was motivated by several reasons mentioned in the literature: i) a large ionic radius allowing for a wide range of coordination numbers, ii) the stereoactivity of the 6s2 lone electron pair leading to a hemidirected or holodirected geometry, iii) a flexible coordination environment, and iv) the possibility to form secondary bonds and unusual non-covalent interactions, such as classic hydrogen bonds and π···π stacking interactions, as well as nonconventional hydrogen bonds and rarely reported tetrel bonds, Pb(lone pair)···π interactions, C–H···Pb agostic-type interactions or hydrogen bonds, and chelate ring stacking interactions. Moreover, the construction of coordination polymers requires the selection of proper ligands acting as linkers, because we are looking for materials exhibiting different network topologies and fluorescence properties, which point to potential applications. The reaction of Pb(NO₃)₂ with 1H-pyrrole-2-carboxylic acid (2prCOOH) leads to the formation of a new four-nuclear Pb(II) polymer, [Pb4(2prCOO)₈(H₂O)]ₙ, which has been characterized by CHN, FT-IR, TG, PL and single-crystal X-ray diffraction methods. In view of the primary Pb–O bonds, Pb1 and Pb2 show hemidirected pentagonal pyramidal geometries, while Pb2 and Pb4 display hemidirected octahedral geometries. The topology of the strongest Pb–O bonds was determined as the (4·8²) fes topology. Taking the secondary Pb–O bonds into account, the coordination number of Pb centres increased, Pb1 exhibited a hemidirected monocapped pentagonal pyramidal geometry, Pb2 and Pb4 exhibited a holodirected tricapped trigonal prismatic geometry, and Pb3 exhibited a holodirected bicapped trigonal prismatic geometry. Moreover, the Pb(II) lone pair stereoactivity was confirmed by DFT calculations. The 2D structure was expanded into 3D by the existence of non-covalent O/C–H···π and Pb···π interactions, which was confirmed by the Hirshfeld surface analysis. The above mentioned interactions improve the rigidity of the structure and facilitate the charge and energy transfer between metal centres, making the polymer a promising luminescent compound.

Keywords: coordination polymers, fluorescence properties, lead(II), lone electron pair stereoactivity, non-covalent interactions

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