Search results for: nonlinear optic

Authors: Anton S. Perin, Vladimir M. Shandarov

Abstract:

Compensation for the nonlinear diffraction of narrow laser beams with wavelength of 532 and the formation of photonic waveguides and waveguide circuits due to the contribution of pyroelectric effect to the nonlinear response of lithium niobate crystal have been experimentally demonstrated. Complete compensation for the linear and nonlinear diffraction broadening of light beams is obtained upon uniform heating of an undoped sample from room temperature to 55 degrees Celsius. An analysis of the light-field distribution patterns and the corresponding intensity distribution profiles allowed us to estimate the spacing for the channel waveguides. The observed behavior of bright soliton beams may be caused by their coherent interaction, which manifests itself in repulsion for anti-phase light fields and in attraction for in-phase light fields. The experimental results of this study showed a fundamental possibility of forming optically complex waveguide structures in lithium niobate crystals with pyroelectric mechanism of nonlinear response. The topology of these structures is determined by the light field distribution on the input face of crystalline sample. The optical induction of channel waveguide elements by interacting spatial solitons makes it possible to design optical systems with a more complex topology and a possibility of their dynamic reconfiguration.

Keywords: self-action, soliton, lithium niobate, piroliton, photorefractive effect, pyroelectric effect

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Authors: Shilpa Khobragade, Carlos Da Silva Granja, Niklas Sandström, Igor Efimov, Victor P. Ostanin, Wouter van der Wijngaart, David Klenerman, Sourav K. Ghosh

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Rapid, label-free and direct detection of pathogenic bacteria is critical for the prevention of disease outbreaks. This paper for the first time attempts to probe the nonlinear acoustic response of quartz crystal resonator (QCR) functionalized with specific DNA aptamers for direct detection and quantification of viable E. coli KCTC 2571 bacteria. DNA aptamers were immobilized through biotin and streptavidin conjugation, onto the gold surface of QCR to capture the target bacteria and the detection was accomplished by shift in amplitude of the peak 3f signal (3 times the drive frequency) upon binding, when driven near fundamental resonance frequency. The developed nonlinear acoustic aptasensor system demonstrated better reliability than conventional resonance frequency shift and energy dissipation monitoring that were recorded simultaneously. This sensing system could directly detect 10⁽⁵⁾ cells/mL target bacteria within 30 min or less and had high specificity towards E. coli KCTC 2571 bacteria as compared to the same concentration of S.typhi bacteria. Aptasensor response was observed for the bacterial suspensions ranging from 10⁽⁵⁾-10⁽⁸⁾ cells/mL. Conclusively, this nonlinear acoustic aptasensor is simple to use, gives real-time output, cost-effective and has the potential for rapid, specific, label-free direction detection of bacteria.

Keywords: acoustic, aptasensor, detection, nonlinear

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Authors: C. Babu Rao, Pandian Chelliah

Abstract:

Owing to their reliability, a number of fluorescent spectra based fiber optic sensors have been developed for detection and identification of hazardous chemicals such as explosives, narcotics etc. In High security regions, such as airports, it is important to monitor simultaneously multiple locations. This calls for deployment of a portable sensor at each location. However, the selectivity and sensitivity of these techniques depends on the spectral resolution of the spectral analyzer. The better the resolution the larger the repertoire of chemicals that can be detected. A portable unit will have limitations in meeting these requirements. Optical fibers can be employed for collecting and transmitting spectral signal from the portable sensor head to a sensitive central spectral analyzer (CSA). For multipoint sensing, optical multiplexing of multiple sensor heads with CSA has to be adopted. However with multiplexing, when one sensor head is connected to CSA, the rest may remain unconnected for the turn-around period. The larger the number of sensor heads the larger this turn-around time will be. To circumvent this imitation, we propose in this paper, an optical encoding methodology to use multiple portable sensor heads connected to a single CSA. Each portable sensor head is assigned an unique address. Spectra of every chemical detected through this sensor head, are encoded by its unique address and can be identified at the CSA end. The methodology proposed is demonstrated through a simulation using Matlab SIMULINK.

Keywords: optical encoding, fluorescence, multipoint sensing

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Authors: Madhu Aneja, Sapna Sharma

Abstract:

Thermal conductivity of ordinary heat transfer fluids is not adequate to meet today’s cooling rate requirements. Nanoparticles have been shown to increase the thermal conductivity and convective heat transfer to the base fluids. One of the possible mechanisms for anomalous increase in the thermal conductivity of nanofluids is the Brownian motions of the nanoparticles in the basefluid. In this paper, the natural convection of incompressible nanofluid over a nonlinear stretching sheet in the presence of magnetic field is studied. The flow and heat transfer induced by stretching sheets is important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. For computational purpose, Finite Element Method is used. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo – Klienstreuer – Li) correlation. In this model effect of Brownian motion on thermal conductivity is considered. The effect of important parameter i.e. nonlinear parameter, volume fraction, Hartmann number, heat source parameter is studied on velocity and temperature. Skin friction and heat transfer coefficients are also calculated for concerned parameters.

Keywords: Brownian motion, convection, finite element method, magnetic field, nanofluid, stretching sheet

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Authors: Kazuma Okada, Tomoaki Hashimoto, Hirokazu Tahara

Abstract:

Recently, the effectiveness of random dither quantization method for linear feedback control systems has been shown in several papers. However, the random dither quantization method has not yet been applied to nonlinear feedback control systems. The objective of this paper is to verify the effectiveness of random dither quantization method for nonlinear feedback control systems. For this purpose, we consider the attitude stabilization problem of satellites using discrete-level actuators. Namely, this paper provides a control method based on the random dither quantization method for stabilizing the attitude of satellites using discrete-level actuators.

Keywords: quantized control, nonlinear systems, random dither quantization

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Authors: Keita Iwai, Isao Tomita

Abstract:

To expand the optical spectrum for use in broadband optical communications, we study the properties of a semiconductor waveguide device with a tapered structure including its third-order optical nonlinearity. Spectral-broadened output by the tapered structure has the potential to create a compact, built-in device for optical communications. Here we deal with a compound semiconductor waveguide, the material of which is the same as that of laser diodes used in the communication systems, i.e., InₓGa₁₋ₓAsᵧP₁₋ᵧ, which has large optical nonlinearity. We confirm that our structure widens the output spectrum sufficiently by controlling its taper form factor while utilizing the large nonlinear refraction of InₓGa₁₋ₓAsᵧP₁₋ᵧ. We also examine the taper effect for nonlinear optical loss.

Keywords: InₓGa₁₋ₓAsᵧP₁₋ᵧ, waveguide, nonlinear refraction, spectral spreading, taper device

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Authors: Areeg Shermaddo

Abstract:

Solar updraft power plants (SUPP) provide a great potential for green and environmentally friendly renewable power generation. An up to 1000 m high chimney represents one of the major parts of each SUPP, which consist of the main shell structure and the stiffening rings. Including the nonlinear material behavior in a simulation of the chimney is computationally a demanding task. However, allowing the formation of cracking in concrete leads to a more economical design of the structure. In this work, an FE model of a SUPP is presented incorporating the nonlinear material behavior. The effect of wind loading intensity on the structural response is explored. Furthermore, the influence of the stiffness of the ring beams on the global behavior is as well investigated. The obtained results indicate that the minimum reinforcement is capable of carrying the tensile stresses provided that the ring beams are rather stiff.

Keywords: ABAQUS, nonlinear analysis, ring beams, SUPP

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Authors: Hussain Adnan Alsalman, Khalid Alhajri, Humoud Alrashidi, Abdulkareem Almakrami, Badie Alguwaisem, Said Alshahrani, Abdullah Alrowaished

Abstract:

Most of the cost of installing a new fiber optic cable is attributed to civil work-trenching-cost. In many cases, information technology departments receive project proposals in their eReview system, but not all projects are visible to everyone. Additionally, if there was no IT scope in the proposed project, it is not likely to be visible to IT. Sometimes it is too late to add IT scope after project budgets have been finalized. Finally, the eReview system is a repository of PDF files for each project, which commits the reviewer to manual work and limits automation potential. This paper details a solution to address the late notification of the eReview system by integrating IT Sites GIS data-sites locations-with land use permit (LUP) data-civil work activity, which is the first step before securing the required land usage authorizations and means no detailed designs for any relevant project before an approved LUP request. To address the manual nature of eReview system, both the LUP System and IT data are using ArcGIS Desktop, which enables the creation of a geoprocessing tool with either Python or Model Builder to automate finding and evaluating potentially usable LUP requests to reduce trenching between two sites in need of a new FOC. To achieve this, a weekly dump was taken from LUP system production data and loaded manually onto ArcMap Desktop. Then a custom tool was developed in model builder, which consisted of a table of two columns containing all the pairs of sites in need of new fiber connectivity. The tool then iterates all rows of this table, taking the sites’ pair one at a time and finding potential LUPs between them, which satisfies the provided search radius. If a group of LUPs was found, an iterator would go through each LUP to find the required civil work between the two sites and the LUP Polyline feature and the distance through the line, which would be counted as cost avoidance if an IT scope had been added. Finally, the tool will export an Excel file named with sites pair, and it will contain as many rows as the number of LUPs, which met the search radius containing trenching and pulling information and cost. As a result, multiple projects have been identified – historical, missed opportunity, and proposed projects. For the proposed project, the savings were about 75% ($750,000) to install a new fiber with the Euclidean distance between Abqaiq GOSP2 and GOSP3 DCOs. In conclusion, the current tool setup identifies opportunities to bundle civil work on single projects at a time and between two sites. More work is needed to allow the bundling of multiple projects between two sites to achieve even more cost avoidance in both capital cost and carbon footprint.

Keywords: GIS, fiber optic cable installation optimization, eliminate redundant civil work, reduce carbon footprint for fiber optic cable installation

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Authors: Khaled Sandjak, Boualem Tiliouine

Abstract:

Structural analysis of flexible pavements has been and still is currently performed using multi-layer elastic theory. However, for thinly surfaced pavements subjected to low to medium volumes of traffics, the importance of non-linear stress-strain behaviour of unbound granular materials (UGM) requires the use of more sophisticated numerical models for structural design and performance of such pavements. In the present work, nonlinear unbound aggregates constitutive model is implemented within an axisymmetric finite element code developed to simulate the nonlinear behaviour of pavement structures including two local aggregates of different mineralogical nature, typically used in Algerian pavements. The performance of the mechanical model is examined about its capability of representing adequately, under various conditions, the granular material non-linearity in pavement analysis. In addition, deflection data collected by falling weight deflectometer (FWD) are incorporated into the analysis in order to assess the sensitivity of critical pavement design criteria and pavement design life to the constitutive model. Finally, conclusions of engineering significance are formulated.

Keywords: FWD backcalculations, finite element simulations, Nonlinear resilient behaviour, pavement response and performance, RLT test results, unbound granular materials

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Authors: Tsegay Giday Woldu, Haibin Zhang, Xin Zhang, Yemane Hailu Fissuh

Abstract:

It is well known that nonlinear conjugate gradient method is one of the widely used first order methods to solve large scale unconstrained smooth optimization problems. Because of the low memory requirement, attractive theoretical features, practical computational efficiency and nice convergence properties, nonlinear conjugate gradient methods have a special role for solving large scale unconstrained optimization problems. Large scale optimization problems are with important applications in practical and scientific world. However, nonlinear conjugate gradient methods have restricted information about the curvature of the objective function and they are likely less efficient and robust compared to some second order algorithms. To overcome these drawbacks, the new modified nonlinear conjugate gradient method is presented. The noticeable features of our work are that the new search direction possesses the sufficient descent property independent of any line search and it belongs to a trust region. Under mild assumptions and standard Wolfe line search technique, the global convergence property of the proposed algorithm is established. Furthermore, to test the practical computational performance of our new algorithm, numerical experiments are provided and implemented on the set of some large dimensional unconstrained problems. The numerical results show that the proposed algorithm is an efficient and robust compared with other similar algorithms.

Keywords: conjugate gradient method, global convergence, large scale optimization, sufficient descent property

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Authors: Mrinal Jana, Geetanjali Panda

Abstract:

In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

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Authors: Ju-Young Hwang, Hyo-Gyoung Kwak

Abstract:

This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical nonlinearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC, high temperature, after-cooling analysis, nonlinear analysis

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Authors: Somayyeh Karimiyan

Abstract:

To evaluate the seismic vulnerability of vital offshore structures with the highest possible precision, Nonlinear Time History Analyses (NLTHA), is the most reliable method. However, since it is very time-consuming, a quick procedure is greatly desired. This paper presents a quick method by combining the Push Over Analysis (POA) and the NLTHA. The POA is preformed first to recognize the more critical members, and then the NLTHA is performed to evaluate more precisely the critical members’ vulnerability. The proposed method has been applied to jacket type structure. Results show that combining POA and NLTHA is a reliable seismic evaluation method, and also that none of the earthquake characteristics alone, can be a dominant factor in vulnerability evaluation.

Keywords: jacket structure, seismic evaluation, push-over and nonlinear time history analyses, critical members

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Authors: Meziane Belkacem

Abstract:

We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Ana Ferreira, Ines Costa, Patricia Polónia, Josué Pereira, Olinda Faria, Pedro Alberto Silva

Abstract:

Introduction: Optical coherence tomography (OCT) and visual field tools are pivotal in evaluating neurological deficits and predicting potential visual improvement following surgical decompression in neurosurgical patients. Despite their clinical significance, a comprehensive understanding of their utility in this context is lacking in the literature. This study aims to elucidate the applications of OCT and visual field assessment, delineating distinct patterns of visual deficit presentations within the studied cohort. Methods: This retrospective analysis considered all adult patients who underwent a single surgery for pituitary adenoma or anterior skull base meningioma with optic nerve involvement, coupled with neuro-ophthalmology evaluation, between July 2020 and January 2023. A minimum follow-up period of 6 months was deemed essential. Results: A total of 24 patients, with a median age of 61, were included in the analysis. Three primary patterns emerged: 1) Low visual field involvement with compromised OCT, 2) High visual field involvement with relatively unaffected OCT, and 3) Significant compromise observed in both OCT and visual fields. Conclusion: This study delineates various findings in OCT and visual field assessments with illustrative examples. Based on the current findings, a prospective cohort will be systematically collected to further investigate and validate these patterns and their prognostic significance, enhancing our understanding of the utility of OCT and visual fields in neurosurgical patients.

Keywords: OCT, neurosurgery, visual field, optic nerve

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Authors: M. H. Korayem, Sh. Ameri, N. Yousefi Lademakhi

Abstract:

To ensure the stability of closed-loop nonlinear model predictive control (NMPC) within a finite horizon, there is a need for appropriate design terminal ingredients, which can be a time-consuming and challenging effort. Otherwise, in order to ensure the stability of the control system, it is necessary to consider an infinite predictive horizon. Increasing the prediction horizon increases computational demand and slows down the implementation of the method. In this study, a new technique has been proposed to ensure system stability without terminal ingredients. This technique has been employed in the design of the NMPC algorithm, leading to a reduction in the computational complexity of designing terminal ingredients and computational burden. The studied system is a wheeled mobile robot (WMR) subjected to non-holonomic constraints. Simulation has been investigated for two problems: trajectory tracking and adjustment mode.

Keywords: wheeled mobile robot, nonlinear model predictive control, stability, without terminal ingredients

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Authors: S. N. Derrar, M. Sekkal-Rahal

Abstract:

The Nonlinear optics (NLO) technique is widely used in the field of biological imaging. In fact, grafting biological entities with a high NLO response on tissues and cells enhances the NLO responses of these latter, and ameliorates, consequently, their biological imaging quality. In this optics, we carried out a theoretical study, in the aim of analyzing the peptide bonds created between alanine amino acid and both unnatural amino acids: L-Dopa and Azatryptophan, respectively. Ramachandran plots have been performed for these systems, and their structural parameters have been analyzed. The NLO responses of these peptides have been reported by calculating the first hyperpolarizability values of all the minima found on the plots. The use of such unnatural amino acids as endogenous probing molecules has been investigated through this study. The Density Functional Theory (DFT) has been used for structural properties, while the Second-order Møller-Plesset Perturbation Theory (MP2) has been employed for the NLO calculations.

Keywords: biological imaging, hyperpolarizability, nonlinear optics, probing molecule

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Authors: Shangerganesh Lingeshwaran

Abstract:

In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: David C. Ni

Abstract:

In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: Abderraouf Gaaloul, Faouzi Msahli

Abstract:

The use of standard sliding mode controller, usually, leads to the appearing of an undesirable chattering phenomenon affecting the control signal. Such problem can be overcome using a higher-order sliding mode controller (HOSMC) which preserves the main properties of the standard sliding mode and deliberately increases the control smoothness. In this paper, we propose a new HOSMC for a class of uncertain multi-input multi-output nonlinear systems. Based on high gain and integral sliding mode paradigms, the established control scheme removes theoretically the chattering phenomenon and provides the stability of the control system. Numerical simulations are developed to show the effectiveness of the proposed controller when applied to solve a control problem of two water levels into a quadruple-tank process.

Keywords: nonlinear systems, sliding mode control, high gain, higher order

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Authors: Dong Sang Yoo

Abstract:

We consider nonlinear uncertain systems such that a priori information of the uncertainties is not available. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound and design a continuous robust control which renders nonlinear uncertain systems ultimately bounded.

Keywords: adaptive control, estimation, Fredholm integral, uncertain system

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Authors: Hocine Hammoum, Karima Bouzelha, Lounis Ziani, Lounis Hamitouche

Abstract:

In this paper, we study a complex structure which is an apartment building surmounted by a reinforced concrete water tank. The tank located on the top floor of the building is a container with capacity of 1000 m³. The building is complex in its design, its calculation and by its behavior under earthquake effect. This structure located in Algiers and aged of 53 years has been subjected to several earthquakes, but the earthquake of May 21^st, 2003 with a magnitude of 6.7 on the Richter scale that struck Boumerdes region at 40 Kms East of Algiers was fatal for it. It was downgraded after an investigation study because the central core sustained serious damage. In this paper, to estimate the degree of its damages, the seismic performance of the structure will be evaluated taking into account the hydrodynamic effect, using a static equivalent nonlinear analysis called pushover.

Keywords: performance analysis, building, reinforced concrete tank, seismic analysis, nonlinear analysis, hydrodynamic, pushover

Procedia PDF Downloads 389

Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

Abstract:

This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Yosra Baaziz, Moez Labidi

Abstract:

Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

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Authors: Ju-young Hwang, Hyo-Gyoung Kwak, Hong Jae Yim

Abstract:

This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical non-linearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, Prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC structures, heat transfer analysis, nonlinear analysis, after-cooling concrete model

Procedia PDF Downloads 336

Authors: Haowen Xi

Abstract:

We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

Abstract:

Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

Abstract:

Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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

Abstract:

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

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

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

Abstract:

In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Heisenberg Ferromagnet equations, soliton equations, equivalence, Lax representation

Procedia PDF Downloads 430