Search results for: Nonlinear optics

Authors: A. Ras, I. Nait Zerrad, N. Benmouna, N. Boumechra

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Use of base isolators in the seismic design of structures has attracted considerable attention in recent years. The major concern in the design of these structures is to have enough lateral stability to resist wind and seismic forces. There are different systems providing such isolation, among them there are friction- pendulum base isolation systems (FPS) which are rather widely applied nowadays involving to both affordable cost and high fundamental periods. These devices are characterised by a stiff resistance against wind loads and to be flexible to the seismic tremors, which make them suitable for different situations. In this paper, a 3D numerical investigation is done considering the seismic response of a twelve-storey steel building retrofitted with a FPS. Fast nonlinear time history analysis (FNA) of Boumerdes earthquake (Algeria, May 2003) is considered for analysis and carried out using SAP2000 software. Comparisons between fixed base, bearing base isolated and braced structures are shown in a tabulated and graphical format. The results of the various alternatives studies to compare the structural response without and with this device of dissipation energy thus obtained were discussed and the conclusions showed the interesting potential of the FPS isolator. This system may to improve the dissipative capacities of the structure without increasing its rigidity in a significant way which contributes to optimize the quantity of steel necessary for its general stability.

Keywords: Steel structure, energy dissipation, friction-pendulum system, nonlinear analysis.

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Authors: Ekprasit Promtun, Sridhar Seshagiri

Abstract:

This paper considers the control of the longitudinal flight dynamics of an F-16 aircraft. The primary design objective is model-following of the pitch rate q, which is the preferred system for aircraft approach and landing. Regulation of the aircraft velocity V (or the Mach-hold autopilot) is also considered, but as a secondary objective. The problem is challenging because the system is nonlinear, and also non-affine in the input. A sliding mode controller is designed for the pitch rate, that exploits the modal decomposition of the linearized dynamics into its short-period and phugoid approximations. The inherent robustness of the SMC design provides a convenient way to design controllers without gain scheduling, with a steady-state response that is comparable to that of a conventional polynomial based gain-scheduled approach with integral control, but with improved transient performance. Integral action is introduced in the sliding mode design using the recently developed technique of “conditional integrators", and it is shown that robust regulation is achieved with asymptotically constant exogenous signals, without degrading the transient response. Through extensive simulation on the nonlinear multiple-input multiple-output (MIMO) longitudinal model of the F-16 aircraft, it is shown that the conditional integrator design outperforms the one based on the conventional linear control, without requiring any scheduling.

Keywords: Sliding-mode Control, Integral Control, Model Following, F-16 Longitudinal Dynamics, Pitch-Rate Control.

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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) Steel02 materials and 2) Pinching4 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 Pinching4 material  was more conservative than that of using Steel02 material in the piping  system.

Keywords: Fragility, T-joint, Piping, Leakage, Sprinkler.

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Authors: Abdelkarim M. Ertiame, D. W. Yu, D. L. Yu, J. B. Gomm

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In this paper, a robust fault detection and isolation (FDI) scheme is developed to monitor a multivariable nonlinear chemical process called the Chylla-Haase polymerization reactor, when it is under the cascade PI control. The scheme employs a radial basis function neural network (RBFNN) in an independent mode to model the process dynamics, and using the weighted sum-squared prediction error as the residual. The Recursive Orthogonal Least Squares algorithm (ROLS) is employed to train the model to overcome the training difficulty of the independent mode of the network. Then, another RBFNN is used as a fault classifier to isolate faults from different features involved in the residual vector. Several actuator and sensor faults are simulated in a nonlinear simulation of the reactor in Simulink. The scheme is used to detect and isolate the faults on-line. The simulation results show the effectiveness of the scheme even the process is subjected to disturbances and uncertainties including significant changes in the monomer feed rate, fouling factor, impurity factor, ambient temperature, and measurement noise. The simulation results are presented to illustrate the effectiveness and robustness of the proposed method.

Keywords: Robust fault detection, cascade control, independent RBF model, RBF neural networks, Chylla-Haase reactor, FDI under closed-loop control.

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Authors: Sh. Foroughi, V. Karamzadeh, M. Packirisamy

Abstract:

This paper presents design and analysis of an electrothermally symmetrical actuated microgripper applicable for performing micro assembly or biological cell manipulation. Integration of micro-optics with microdevice leads to achieve extremely precise control over the operation of the device. Geometry, material, actuation, control, accuracy in measurement and temperature distribution are important factors which have to be taken into account for designing the efficient microgripper device. In this work, analyses of four different geometries are performed by means of COMSOL Multiphysics 5.2 with implementing Finite Element Methods. Then, temperature distribution along the fingertip, displacement of gripper site as well as optical efficiency vs. displacement and electrical potential are illustrated. Results show in addition to the industrial application of this device, the usage of that as a cell manipulator is possible.

Keywords: Electro thermal actuator, MEMS, Microgripper, MOEMS.

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Authors: Roberto Iglesias, Theocharis Kyriacou, Ulrich Nehmzow, Steve Billings

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Fundamental sensor-motor couplings form the backbone of most mobile robot control tasks, and often need to be implemented fast, efficiently and nevertheless reliably. Machine learning techniques are therefore often used to obtain the desired sensor-motor competences. In this paper we present an alternative to established machine learning methods such as artificial neural networks, that is very fast, easy to implement, and has the distinct advantage that it generates transparent, analysable sensor-motor couplings: system identification through nonlinear polynomial mapping. This work, which is part of the RobotMODIC project at the universities of Essex and Sheffield, aims to develop a theoretical understanding of the interaction between the robot and its environment. One of the purposes of this research is to enable the principled design of robot control programs. As a first step towards this aim we model the behaviour of the robot, as this emerges from its interaction with the environment, with the NARMAX modelling method (Nonlinear, Auto-Regressive, Moving Average models with eXogenous inputs). This method produces explicit polynomial functions that can be subsequently analysed using established mathematical methods. In this paper we demonstrate the fidelity of the obtained NARMAX models in the challenging task of robot route learning; we present a set of experiments in which a Magellan Pro mobile robot was taught to follow four different routes, always using the same mechanism to obtain the required control law.

Keywords: Mobile robotics, system identification, non-linear modelling, NARMAX.

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Authors: G. Sonfack, J. Mbihi, B. Lonla Moffo

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This paper presents an optimal duty-cycle modulation (ODCM) scheme for analog-to-digital conversion (ADC) systems. The overall ODCM-Based ADC problem is decoupled into optimal DCM and digital filtering sub-problems, while taking into account constraints of mutual design parameters between the two. Using a set of three lemmas and four morphological theorems, the ODCM sub-problem is modelled as a nonlinear cost function with nonlinear constraints. Then, a weighted least p^th norm of the error between ideal and predicted frequency responses is used as a cost function for the digital filtering sub-problem. In addition, MATLAB fmincon and MATLAB iirlnorm tools are used as optimal DCM and least p^th norm solvers respectively. Furthermore, the virtual simulation scheme of an overall prototyping ODCM-based ADC system is implemented and well tested with the help of Simulink tool according to relevant set of design data, i.e., 3 KHz of modulating bandwidth, 172 KHz of maximum modulation frequency and 25 MHZ of sampling frequency. Finally, the results obtained and presented show that the ODCM-based ADC achieves under 3 KHz of modulating bandwidth: 57 dBc of SINAD (signal-to-noise and distorsion), 58 dB of SFDR (Surpious free dynamic range) -80 dBc of THD (total harmonic distorsion), and 10 bits of minimum resolution. These performance levels appear to be a great challenge within the class of oversampling ADC topologies, with 2^nd order IIR (infinite impulse response) decimation filter.

Keywords: Digital IIR filter, morphological lemmas and theorems, optimal DCM-based DAC, virtual simulation, weighted least pth norm.

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Authors: L. Pina, M. Mika, R. Havlikova, M. Landova, L. Sveda, R. Hudec, V. Marsikova, A. Inneman

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We developed a non-contact method for the in-situ monitoring of the thermal forming of glass and Si foils to optimize the manufacture of mirrors for high-resolution space x-ray telescopes. Their construction requires precise and light-weight segmented optics with angular resolution better than 5 arcsec. We used 75x25 mm Desag D263 glass foils 0.75 mm thick and 0.6 mm thick Si foils. The glass foils were shaped by free slumping on a frame at viscosities in the range of 109.3-1012 dPa·s, the Si foils by forced slumping above 1000°C. Using a Nikon D80 digital camera, we took snapshots of a foil-s shape every 5 min during its isothermal heat treatment. The obtained results we can use for computer simulations. By comparing the measured and simulated data, we can more precisely define material properties of the foils and optimize the forming technology.

Keywords: Glass, in-situ monitoring, silicone, thermal forming, x-ray telescope

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Authors: D. Koren, V. Kilar

Abstract:

The modern energy-efficient houses are often founded on a thermal insulation (TI) layer placed under the building’s RC foundation slab.The purpose of the paper is to identify the potential problems of the buildings founded on TI layer from the seismic point of view. The two main goals of the study were to assess the seismic behavior of such buildings, and to search for the critical structural parameters affecting the response of the superstructure as well as of the extruded polystyrene (XPS) layer. As a test building a multi-storeyed RC frame structure with and without the XPS layer under the foundation slab has been investigated utilizing nonlinear dynamic (time-history) and static (pushover) analyses. The structural response has been investigated with reference to the following performance parameters: i) Building’s lateral roof displacements, ii) Edge compressive and shear strains of the XPS, iii) Horizontal accelerations of the superstructure, iv) Plastic hinge patterns of the superstructure, v) Part of the foundation in compression, and vi) Deformations of the underlying soil and vertical displacements of the foundation slab (i.e. identifying the potential uplift). The results have shown that in the case of higher and stiff structures lying on firm soil the use of XPS under the foundation slab might induce amplified structural peak responses compared to the building models without XPS under the foundation slab. The analysis has revealed that the superstructure as well as the XPS response is substantially affected by the stiffness of the foundation slab.

Keywords: Extruded polystyrene (XPS), foundation on thermal insulation, energy-efficient buildings, nonlinear seismic analysis, seismic response, soil–structure interaction.

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Authors: D. D. Wang, J.C. Lam, Z. H. Mai

Abstract:

Controlled modification of appropriate sharpness for nanotips is of paramount importance to develop novel materials and functional devices at a nanometer resolution. Herein, we present a reliable and unique strategy of laser irradiation enhanced physicochemical etching to manufacture super sharp tungsten tips with reproducible shape and dimension as well as high yields (~80%). The corresponding morphology structure evolution of tungsten tips and laser-tip interaction mechanisms were systematically investigated and discussed using field emission scanning electron microscope (SEM) and physical optics statistics method with different fluences under 532 nm laser irradiation. This work paves the way for exploring more accessible metallic tips applications with tunable apex diameter and aspect ratio, and, furthermore, facilitates the potential sharpening enhancement technique for other materials used in a variety of nanoscale devices.

Keywords: Tungsten tip sharpening, Laser irradiation, Physicochemical etching, Light-matter interaction.

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Authors: Athanasios Theoharidis, Thomas Kamalakis, Ioannis Neokosmidis, Thomas Sphicopoulos

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In this paper, the application of the Mode Matching (MM) method in the case of photonic crystal waveguide discontinuities is presented. The structure under consideration is divided into a number of cells, which supports a number of guided and evanescent modes. These modes can be calculated numerically by an alternative formulation of the plane wave expansion method for each frequency. A matrix equation is then formed relating the modal amplitudes at the beginning and at the end of the structure. The theory is highly efficient and accurate and can be applied to study the transmission sensitivity of photonic crystal devices due to fabrication tolerances. The accuracy of the MM method is compared to the Finite Difference Frequency Domain (FDFD) and the Adjoint Variable Method (AVM) and good agreement is observed.

Keywords: Optical Communications, Integrated Optics, Photonic Crystals, Optical Waveguide Discontinuities.

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Authors: Anamika Jain, A. S. Thoke, R. N. Patel

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This paper addresses the problems encountered by conventional distance relays when protecting double-circuit transmission lines. The problems arise principally as a result of the mutual coupling between the two circuits under different fault conditions; this mutual coupling is highly nonlinear in nature. An adaptive protection scheme is proposed for such lines based on application of artificial neural network (ANN). ANN has the ability to classify the nonlinear relationship between measured signals by identifying different patterns of the associated signals. One of the key points of the present work is that only current signals measured at local end have been used to detect and classify the faults in the double circuit transmission line with double end infeed. The adaptive protection scheme is tested under a specific fault type, but varying fault location, fault resistance, fault inception angle and with remote end infeed. An improved performance is experienced once the neural network is trained adequately, which performs precisely when faced with different system parameters and conditions. The entire test results clearly show that the fault is detected and classified within a quarter cycle; thus the proposed adaptive protection technique is well suited for double circuit transmission line fault detection & classification. Results of performance studies show that the proposed neural network-based module can improve the performance of conventional fault selection algorithms.

Keywords: Double circuit transmission line, Fault detection and classification, High impedance fault and Artificial Neural Network.

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Authors: Najm M. Al-Hosiny

Abstract:

We theoretically investigate the effects of frequency detuning and injection power on the nonlinear dynamics of DFB lasers under dual external optical injection.

Keywords: Optical injection, DFB laser, frequency detuning, injection power.

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Authors: Muhammad Sameer Ahmed, Piotr Remlein, Tansal Gucluoglu

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The technique called as Generalized frequency division multiplexing (GFDM) used in the free space optical channel can be a good option for implementation free space optical communication systems. This technique has several strengths e.g. good spectral efficiency, low peak-to-average power ratio (PAPR), adaptability and low co-channel interference. In this paper, the impact of weather conditions such as haze, rain and fog on GFDM over the gamma-gamma channel model is discussed. A Trade off between link distance and system performance under intense weather conditions is also analysed. The symbol error probability (SEP) of GFDM over the gamma-gamma turbulence channel is derived and verified with the computer simulations.

Keywords: Free space optics, generalized frequency division multiplexing, weather conditions, gamma gamma distribution.

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Authors: R .Lassoued, M. Guenfoud

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An accurate procedure to determine free vibrations of beams and plates is presented. The natural frequencies are exact solutions of governing vibration equations witch load to a nonlinear homogeny system. The bilinear and linear structures considered simulate a bridge. The dynamic behavior of this one is analyzed by using the theory of the orthotropic plate simply supported on two sides and free on the two others. The plate can be excited by a convoy of constant or harmonic loads. The determination of the dynamic response of the structures considered requires knowledge of the free frequencies and the shape modes of vibrations. Our work is in this context. Indeed, we are interested to develop a self-consistent calculation of the Eigen frequencies. The formulation is based on the determination of the solution of the differential equations of vibrations. The boundary conditions corresponding to the shape modes permit to lead to a homogeneous system. Determination of the noncommonplace solutions of this system led to a nonlinear problem in Eigen frequencies. We thus, develop a computer code for the determination of the eigenvalues. It is based on a method of bisection with interpolation whose precision reaches 10 -12. Moreover, to determine the corresponding modes, the calculation algorithm that we develop uses the method of Gauss with a partial optimization of the "pivots" combined with an inverse power procedure. The Eigen frequencies of a plate simply supported along two opposite sides while considering the two other free sides are thus analyzed. The results could be generalized with the case of a beam by regarding it as a plate with low width. We give, in this paper, some examples of treated cases. The comparison with results presented in the literature is completely satisfactory.

Keywords: Free frequencies, beams, rectangular plates.

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Authors: Bhanu Gupta, Sanjay K. Srivastava

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In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.

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Authors: Mihai Caramihai, Irina Severin

Abstract:

Bioprocesses are appreciated as difficult to control because their dynamic behavior is highly nonlinear and time varying, in particular, when they are operating in fed batch mode. The research objective of this study was to develop an appropriate control method for a complex bioprocess and to implement it on a laboratory plant. Hence, an intelligent control structure has been designed in order to produce biomass and to maximize the specific growth rate.

Keywords: Fed batch bioprocess, mass-balance model, fuzzy control

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Authors: Annamária Käferné Rácz, Bence Jáger, Balázs Kövesdi, László Dunai

Abstract:

Due to the numerous advantages of steel corrugated web girders, its application field is growing for bridges as well as for buildings. The global stability behavior of such girders is significantly larger than those of conventional I-girders with flat web, thus the application of the structural steel material can be significantly reduced. Design codes and specifications do not provide clear and complete rules or recommendations for the determination of the lateral torsional buckling (LTB) resistance of corrugated web girders. Therefore, the authors made a thorough investigation regarding the LTB resistance of the corrugated web girders. Finite element (FE) simulations have been performed to develop new design formulas for the determination of the LTB resistance of trapezoidally corrugated web girders. FE model is developed considering geometrical and material nonlinear analysis using equivalent geometric imperfections (GMNI analysis). The equivalent geometric imperfections involve the initial geometric imperfections and residual stresses coming from rolling, welding and flame cutting. Imperfection sensitivity analysis was performed to determine the necessary magnitudes regarding only the first eigenmodes shape imperfections. By the help of the validated FE model, an extended parametric study is carried out to investigate the LTB resistance for different trapezoidal corrugation profiles. First, the critical moment of a specific girder was calculated by FE model. The critical moments from the FE calculations are compared to the previous analytical calculation proposals. Then, nonlinear analysis was carried out to determine the ultimate resistance. Due to the numerical investigations, new proposals are developed for the determination of the LTB resistance of trapezoidally corrugated web girders through a modification factor on the design method related to the conventional flat web girders.

Keywords: Critical moment, FE modeling, lateral torsional buckling, trapezoidally corrugated web girders.

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Authors: Mihai Caramihai Ana A Chirvase, Irina Severin

Abstract:

Bioprocesses are appreciated as difficult to control because their dynamic behavior is highly nonlinear and time varying, in particular, when they are operating in fed batch mode. The research objective of this study was to develop an appropriate control method for a complex bioprocess and to implement it on a laboratory plant. Hence, an intelligent control structure has been designed in order to produce biomass and to maximize the specific growth rate.

Keywords: Fed batch bioprocess, mass-balance model, fuzzy control.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota-s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations.

Keywords: (3+1)-dimensional breaking soliton equation, Hirota'sbilinear form.

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Authors: Anant Kumar Singh, Sunil Jha, Pulak M. Pandey

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A novel nanofinishing process using improved ball end magnetorheological (MR) finishing tool was developed for finishing of flat as well as 3D surfaces of ferromagnetic and non ferromagnetic workpieces. In this process a magnetically controlled ball end of smart MR polishing fluid is generated at the tip surface of the tool which is used as a finishing medium and it is guided to follow the surface to be finished through computer controlled 3-axes motion controller. The experiments were performed on ferromagnetic workpiece surface in the developed MR finishing setup to study the effect of finishing time on final surface roughness. The performance of present finishing process on final finished surface roughness was studied. The surface morphology was observed under scanning electron microscopy and atomic force microscope. The final surface finish was obtained as low as 19.7 nm from the initial surface roughness of 142.9 nm. The outcome of newly developed finishing process can be found useful in its applications in aerospace, automotive, dies and molds manufacturing industries, semiconductor and optics machining etc.

Keywords: Ball end MR finishing tool, Magnetorheological finishing, Nanofinishing

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Authors: A. Elakkary, A. Echchatbi, N. Elalami

Abstract:

In this paper, we are interested in attitude control of a satellite, which using wheels of reaction, by state feedback. First, we develop a method allowing us to put the control and its integral in the state-feedback form. Then, by using the theorem of Gronwall- Bellman, we put the sufficient conditions so that the nonlinear system modeling the satellite is stabilisable and observed by state feedback.

Keywords: Satellite, attitude control, state feedback, attitude stabilization.

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Authors: Sergio Pérez-López, Daniel Tarrazó-Serrano, José M. Fuster, Pilar Candelas, Constanza Rubio

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Fresnel Zone Plates (FZPs) are widely used in many areas, such as optics, microwaves or acoustics. On the design of FZPs, plane wave incidence is typically considered, but that is not usually the case in ultrasounds, especially in applications where a piston emitter is placed at a certain distance from the lens. In these cases, having control of the focal distance is very important, and with the usual Fresnel equation a focal displacement from the theoretical distance is observed due to the plane wave supposition. In this work, a comparison between FZP with plane wave incidence design and FZP with point source design in the case of piston emitter is presented. Influence of the main parameters of the piston in the final focalization profile has been studied. Numerical models and experimental results are shown, and they prove that when spherical wave incidence is considered for the piston case, it is possible to have a fine control of the focal distance in comparison with the classical design method.

Keywords: Focusing, Fresnel zone plate, ultrasound, spherical wave incidence, piston emitter.

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included.

Keywords: Population model, Stability, Hopf bifurcation, Delay, Global Hopf bifurcation.

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Authors: Oleg A. Romanovskii, Vladimir D. Burlakov, Sergey I. Dolgii, Olga V. Kharchenko, Alexey A. Nevzorov, Alexey V. Nevzorov

Abstract:

The paper presents the results of DIAL measurements of the vertical ozone distribution. The ozone lidar operate as part of the measurement complex at Siberian Lidar Station (SLS) of V.E. Zuev Institute of Atmospheric Optics SB RAS, Tomsk (56.5ºN; 85.0ºE) and designed for study of the vertical ozone distribution in the upper troposphere–lower stratosphere. Most suitable wavelengths for measurements of ozone profiles are selected. We present an algorithm for retrieval of vertical distribution of ozone with temperature and aerosol correction during DIAL lidar sounding of the atmosphere. The temperature correction of ozone absorption coefficients is introduced in the software to reduce the retrieval errors. Results of lidar measurement at wavelengths of 299 and 341 nm agree with model estimates, which point to acceptable accuracy of ozone sounding in the 6–18 km altitude range.

Keywords: Lidar, ozone distribution, atmosphere, DIAL.

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Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

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Authors: Stephan Rupp, Matthias Elter, Michael Breitung, Walter Zink, Christian Küblbeck

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Camera calibration is an indispensable step for augmented reality or image guided applications where quantitative information should be derived from the images. Usually, a camera calibration is obtained by taking images of a special calibration object and extracting the image coordinates of projected calibration marks enabling the calculation of the projection from the 3d world coordinates to the 2d image coordinates. Thus such a procedure exhibits typical steps, including feature point localization in the acquired images, camera model fitting, correction of distortion introduced by the optics and finally an optimization of the model-s parameters. In this paper we propose to extend this list by further step concerning the identification of the optimal subset of images yielding the smallest overall calibration error. For this, we present a Monte Carlo based algorithm along with a deterministic extension that automatically determines the images yielding an optimal calibration. Finally, we present results proving that the calibration can be significantly improved by automated image selection.

Keywords: Camera Calibration, Discrete Optimization, Monte Carlo Method.

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Authors: Helle Hein, Ülo Lepik

Abstract:

A gradient learning method to regulate the trajectories of some nonlinear chaotic systems is proposed. The method is motivated by the gradient descent learning algorithms for neural networks. It is based on two systems: dynamic optimization system and system for finding sensitivities. Numerical results of several examples are presented, which convincingly illustrate the efficiency of the method.

Keywords: Chaos, Dynamical Systems, Learning, Neural Networks

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

Abstract:

In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: Bifurcation, heteroclinic orbits, steady state, traveling wave.

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Authors: Mohammad Aminnia, Mahmood Hosseini

Abstract:

Environmental and functional conditions, sometimes, necessitate the architectural plan of the building to be asymmetric, and this result in an asymmetric structure. In such cases finding an optimal pattern for locating the components of lateral load bearing system, including shear walls, in the building’s plan is desired. In case of shear wall in addition to the location the shape of the wall cross-section is also an effective factor. Various types of shear walls and their proper layout might come effective in better stiffness distribution and more appropriate seismic response of the building. Several studies have been conducted in the context of analysis and design of shear walls; however, few studies have been performed on making decisions for the location and form of shear walls in multistory buildings, especially those with irregular plan. In this study, an attempt has been made to obtain the most reliable seismic behavior of multi-story reinforced concrete vertically chamfered buildings by using more appropriate shear walls form and arrangement in 7-, 10-, 12-, and 15-stoy buildings. The considered forms and arrangements include common rectangular walls and L-, T-, U- and Z-shaped plan, located as the core or in the outer frames of the building structure. Comparison of seismic behaviors of the buildings, including maximum roof displacement and particularly formation of plastic hinges and their distribution in the buildings’ structures, have been done based on the results of a series of nonlinear time history analyses, by using a set of selected earthquake records. Results show that shear walls with U-shaped cross-section, placed as the building central core, and also walls with Z-shaped cross-section, placed at the corners give the building more reliable seismic behavior.

Keywords: Vertically chamfered buildings, non-linear time history analyses, L-, T-, U- and Z-shaped plan walls.

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