Search results for: nonlinear optical lattice

Authors: Pavlo Selyshchev

Abstract:

Irradiated material is a typical example of a complex system with nonlinear coupling between its elements. During irradiation the radiation damage is developed and this development has bifurcations and qualitatively different kinds of behavior. The accumulation of primary defects in irradiated crystals is considered in frame work of nonlinear evolution of complex system. The thermo-concentration nonlinear feedback is carried out as a mechanism of self-oscillation development. It is shown that there are two ways of the defect density evolution under stationary irradiation. The first is the accumulation of defects; defect density monotonically grows and tends to its stationary state for some system parameters. Another way that takes place for opportune parameters is the development of self-oscillations of the defect density. The stationary state, its stability and type are found. The bifurcation values of parameters (environment temperature, defect generation rate, etc.) are obtained. The frequency of the selfoscillation and the conditions of their development is found and rated. It is shown that defect density, heat fluxes and temperature during self-oscillations can reach much higher values than the expected steady-state values. It can lead to a change of typical operation and an accident, e.g. for nuclear equipment.

Keywords: Irradiation, Primary Defects, Solids, Self-oscillation.

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Authors: Sapan Mohan Saini

Abstract:

We report the electronic structure and optical properties of NdF3 compound. Our calculations are based on density functional theory (DFT) using the full potential linearized augmented plane wave (FPLAPW) method with the inclusion of spin orbit coupling. We employed the local spin density approximation (LSDA) and Coulomb-corrected local spin density approximation, known for treating the highly correlated 4f electrons properly, is able to reproduce the correct insulating ground state. We find that the standard LSDA approach is incapable of correctly describing the electronic properties of such materials since it positions the f-bands incorrectly resulting in an incorrect metallic ground state. On the other hand, LSDA + U approximation, known for treating the highly correlated 4f electrons properly, is able to reproduce the correct insulating ground state. Interestingly, however, we do not find any significant differences in the optical properties calculated using LSDA, and LSDA + U suggesting that the 4f electrons do not play a decisive role in the optical properties of these compounds. The reflectivity for NdF3 compound stays low till 7 eV which is consistent with their large energy gaps. The calculated energy gaps are in good agreement with experiments. Our calculated reflectivity compares well with the experimental data and the results are analyzed in the light of band to band transitions.

Keywords: FPLAPW Method, optical properties, rare earthtrifluorides LSDA+U

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Authors: Ehsan Mahdavi

Abstract:

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

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Authors: M. M. Hasan, A. S. M. A. Haseeb, R. Saidur, H. H. Masjuki

Abstract:

In this investigation, anatase TiO2 thin films were grown by radio frequency magnetron sputtering on glass substrates at a high sputtering pressure and room temperature. The anatase films were then annealed at 300-600 °C in air for a period of 1 hour. To examine the structure and morphology of the films, X-ray diffraction (XRD) and atomic force microscopy (AFM) methods were used respectively. From X-ray diffraction patterns of the TiO2 films, it was found that the as-deposited film showed some differences compared with the annealed films and the intensities of the peaks of the crystalline phase increased with the increase of annealing temperature. From AFM images, the distinct variations in the morphology of the thin films were also observed. The optical constants were characterized using the transmission spectra of the films obtained by UV-VIS-IR spectrophotometer. Besides, optical thickness of the film deposited at room temperature was calculated and cross-checked by taking a cross-sectional image through SEM. The optical band gaps were evaluated through Tauc model. It was observed that TiO2 films produced at room temperatures exhibited high visible transmittance and transmittance decreased slightly with the increase of annealing temperatures. The films were found to be crystalline having anatase phase. The refractive index of the films was found from 2.31-2.35 in the visible range. The extinction coefficient was nearly zero in the visible range and was found to increase with annealing temperature. The allowed indirect optical band gap of the films was estimated to be in the range from 3.39 to 3.42 eV which showed a small variation. The allowed direct band gap was found to increase from 3.67 to 3.72 eV. The porosity was also found to decrease at a higher annealing temperature making the film compact and dense.

Keywords: Titanium dioxide, RF reactive sputtering, Structuralproperties, Surface morphology, Optical properties.

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Authors: Andrey V. Timofeev

Abstract:

This paper presents development results of the method of seismoacoustic activity monitoring based on usage vibrosensitive properties of optical fibers. Analysis of Rayleigh backscattering radiation parameters changes, which take place due to microscopic seismoacoustic impacts on the optical fiber, allows to determine seismoacoustic emission sources positions and to identify their types. Results of using this approach are successful for complex monitoring of railways.

Keywords: C-OTDR systems, monitoring of railways, Rayleigh backscattering.

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Authors: Andreas Körtge, Susanne Stählke, Regina Lange, Mario Birkholz, Mirko Fraschke, Katrin Schulz, Barbara Nebe, Patrick Elter

Abstract:

A major challenge in biomaterials research is the regulation of protein adsorption which is a key factor for controlling the subsequent cell adhesion at implant surfaces. The aim of the present study was to control the adsorption of fibronectin (FN) and the attachment of MG-63 osteoblasts with an electronic nanostructure. Shallow doping line lattices with a period of 260 nm were produced for this purpose by implantation of phosphorous in silicon wafers. Protein coverage was determined after incubating the substrate with FN by means of an immunostaining procedure and the measurement of the fluorescence intensity with a TECAN analyzer. We observed an increased amount of adsorbed FN on the nanostructure compared to control substrates. MG-63 osteoblasts were cultivated for 24h on FN-incubated substrates and their morphology was assessed by SEM. Preferred orientation and elongation of the cells in direction of the doping lattice lines was observed on FN-coated nanostructures.

Keywords: Cell adhesion, electronic nanostructures, doping lattice, fibronectin, MG-63 osteoblasts, protein adsorption.

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Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia

Abstract:

Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.

Keywords: Chaos, adaptive control, nonlinear control, Chua's circuit.

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Authors: Shiyang Zhu, G. Q. Lo, D. L. Kwong

Abstract:

Silicon photonics has generated an increasing interest in recent years mainly for optical communications optical interconnects in microelectronic circuits or bio-sensing applications. The development of elementary passive and active components (including detectors and modulators), which are mainly fabricated on the silicon on insulator platform for CMOS-compatible fabrication, has reached such a performance level that the integration challenge of silicon photonics with microelectronic circuits should be addressed. Since crystalline silicon can only be grown from another silicon crystal, making it impossible to deposit in this state, the optical devices are typically limited to a single layer. An alternative approach is to integrate a photonic layer above the CMOS chip using back-end CMOS fabrication process. In this paper, various materials, including silicon nitride, amorphous silicon, and polycrystalline silicon, for this purpose are addressed.

Keywords: Silicon photonics, CMOS, Integration.

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Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: Anton Stadler, Thorsten Ike

Abstract:

In this paper, we present a video based smoke detection algorithm based on TVL1 optical flow estimation. The main part of the algorithm is an accumulating system for motion angles and upward motion speed of the flow field. We optimized the usage of TVL1 flow estimation for the detection of smoke with very low smoke density. Therefore, we use adapted flow parameters and estimate the flow field on difference images. We show in theory and in evaluation that this improves the performance of smoke detection significantly. We evaluate the smoke algorithm using videos with different smoke densities and different backgrounds. We show that smoke detection is very reliable in varying scenarios. Further we verify that our algorithm is very robust towards crowded scenes disturbance videos.

Keywords: Low density, optical flow, upward smoke motion, video based smoke detection.

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Authors: Chidentree Treesatayapun

Abstract:

A direct adaptive controller for a class of unknown nonlinear discrete-time systems is presented in this article. The proposed controller is constructed by fuzzy rules emulated network (FREN). With its simple structure, the human knowledge about the plant is transferred to be if-then rules for setting the network. These adjustable parameters inside FREN are tuned by the learning mechanism with time varying step size or learning rate. The variation of learning rate is introduced by main theorem to improve the system performance and stabilization. Furthermore, the boundary of adjustable parameters is guaranteed through the on-line learning and membership functions properties. The validation of the theoretical findings is represented by some illustrated examples.

Keywords: Neuro-Fuzzy, learning algorithm, nonlinear discrete time.

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Authors: V. Ten

Abstract:

An approach of design of stable of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers. Theoretical part presents an analysis of designed nonlinear second-order control systems. As more important the integrators in series, canonical controllable form and Jordan forms are considered. The analysis resumes that due to added controllers systems become stable and insensitive to any disturbance of parameters. Experimental part presents MATLAB simulation of design of control systems of epidemic spread, aircrafts angular motion and submarine depth. The results of simulation confirm the efficiency of offered method of design. KeywordsCatastrophes, robust control, simulation, uncertain parameters.

Keywords: Catastrophes, robust control, simulation, uncertain parameters.

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Authors: S. Khademi, A. Darudi, Z. Abbasi

Abstract:

One of the main limitations for the resolution of optical instruments is the size of the sensor-s pixels. In this paper we introduce a new sub pixel resolution algorithm to enhance the resolution of images. This method is based on the analysis of multiimages which are fast recorded during the fine relative motion of image and pixel arrays of CCDs. It is shown that by applying this method for a sample noise free image one will enhance the resolution with 10-14 order of error.

Keywords: Sub Pixel Resolution, Moving Pixels, CCD, Image, Optical Instrument.

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Authors: R. O. Rominu, C. Sinescu, D.M. Pop, M. Hughes, A. Bradu, M. Rominu, A. Gh. Podoleanu

Abstract:

Bonding has become a routine procedure in several dental specialties – from prosthodontics to conservative dentistry and even orthodontics. In many of these fields it is important to be able to investigate the bonded interfaces to assess their quality. All currently employed investigative methods are invasive, meaning that samples are destroyed in the testing procedure and cannot be used again. We have investigated the interface between human enamel and bonded ceramic brackets non-invasively, introducing a combination of new investigative methods – optical coherence tomography (OCT), fluorescence OCT and confocal microscopy (CM). Brackets were conventionally bonded on conditioned buccal surfaces of teeth. The bonding was assessed using these methods. Three dimensional reconstructions of the detected material defects were developed using manual and semi-automatic segmentation. The results clearly prove that OCT, fluorescence OCT and CM are useful in orthodontic bonding investigations.

Keywords: Optical coherence tomography, Confocal Microscopy, Orthodontic Bonding.

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Authors: Satyasen Panda, Urmila Bhanja

Abstract:

This paper presents a SAC-OCDMA code with zero cross correlation property to minimize the Multiple Access Interface (MAI) as New Zero Cross Correlation code (NZCC), which is found to be more scalable compared to the other existing SAC-OCDMA codes. This NZCC code is constructed using address segment and data segment. In this work, the proposed NZCC code is implemented in an optical system using the Opti-System software for the spectral amplitude coded optical code-division multiple-access (SAC-OCDMA) scheme. The main contribution of the proposed NZCC code is the zero cross correlation, which reduces both the MAI and PIIN noises. The proposed NZCC code reveals properties of minimum cross-correlation, flexibility in selecting the code parameters and supports a large number of users, combined with high data rate and longer fiber length. Simulation results reveal that the optical code division multiple access system based on the proposed NZCC code accommodates maximum number of simultaneous users with higher data rate transmission, lower Bit Error Rates (BER) and longer travelling distance without any signal quality degradation, as compared to the former existing SAC-OCDMA codes.

Keywords: Cross Correlation, Optical Code Division Multiple Access, Spectral Amplitude Coding Optical Code Division Multiple Access, Multiple Access Interference, Phase Induced Intensity Noise, New Zero Cross Correlation code.

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Authors: Gorazd Karer, Igor Skrjanc, Borut Zupancic

Abstract:

The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.

Keywords: Batch reactor, fuzzy clustering, hybrid systems, identification, nonlinear systems, PWA systems.

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Authors: Marco Soares dos Santos, Camila Nicola Boeri, Jorge Augusto Ferreira, Fernando Neto da Silva

Abstract:

The highly nonlinear characteristics of drying processes have prompted researchers to seek new nonlinear control solutions. However, the relation between the implementation complexity, on-line processing complexity, reliability control structure and controller-s performance is not well established. The present paper proposes high performance nonlinear fuzzy controllers for a real-time operation of a drying machine, being developed under a consistent match between those issues. A PCI-6025E data acquisition device from National Instruments® was used, and the control system was fully designed with MATLAB® / SIMULINK language. Drying parameters, namely relative humidity and temperature, were controlled through MIMOs Hybrid Bang-bang+PI (BPI) and Four-dimensional Fuzzy Logic (FLC) real-time-based controllers to perform drying tests on biological materials. The performance of the drying strategies was compared through several criteria, which are reported without controllers- retuning. Controllers- performance analysis has showed much better performance of FLC than BPI controller. The absolute errors were lower than 8,85 % for Fuzzy Logic Controller, about three times lower than the experimental results with BPI control.

Keywords: Drying control, Fuzzy logic control, Intelligent temperature-humidity control.

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Authors: T.R. Sahroni, S. Sulaiman, I. Romli, M.R. Salleh, H.A. Ariff

Abstract:

The thermal expansion behaviour of silicon carbide (SCS-2) fibre reinforced 6061 aluminium matrix composite subjected to the influenced thermal mechanical cycling (TMC) process were investigated. The thermal stress has important effect on the longitudinal thermal expansion coefficient of the composites. The present paper used experimental data of the thermal expansion behaviour of a SiC/Al composite for temperatures up to 370°C, in which their data was used for carrying out modelling of theoretical predictions.

Keywords: Nonlinear, thermal, fibre reinforced, metal matrixcomposites

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Authors: Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad, Israr Ahmad

Abstract:

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.

Keywords: Nonlinear Active Control, Chen and Tigan Chaotic systems, Lyapunov Stability theory, Synchronization.

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Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

Abstract:

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

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Authors: Chundong Li, V. V. Neshchimenko, M. M. Mikhailov

Abstract:

The effect of the modification of ZnO powders by ZrO₂, Al₂O₃, TiO₂, SiO₂, CeO₂ and Y₂O₃ nanoparticles with a concentration of 1-30 wt % is investigated by diffuse reflectance spectra within the wavelength range 200 to 2500 nm before and after 100 keV proton and electron irradiation. It has been established that the introduction of nanoparticles ZrO₂, Al₂O₃ enhances the optical stability of the pigments under proton irradiation, but reduces it under electron irradiation. Modifying with TiO₂, SiO₂, CeO₂, Y₂O₃ nanopowders leads to decrease radiation stability in both types of irradiation. Samples modified by 5 wt. % of ZrO₂ nanoparticles have the highest stability of optical properties after proton exposure. The degradation of optical properties under electron irradiation is not high for this concentration of nanoparticles. A decrease in the absorption of pigments modified with nanoparticles proton exposure is determined by a decrease in the intensity of bands located in the UV and visible regions. After electron exposure the absorption bands have in the whole spectrum range.

Keywords: Irradiation, nanopowders, radiation stability, zinc oxide.

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Authors: Ibrahim F. Jasim

Abstract:

This paper presents a new stable robust adaptive controller and observer design for a class of nonlinear systems that contain i. Coupling of unmeasured states and unknown parameters ii. Unknown dead zone at the system actuator. The system is firstly cast into a modified form in which the observer and parameter estimation become feasible. Then a stable robust adaptive controller, state observer, parameter update laws are derived that would provide global adaptive system stability and desirable performance. To validate the approach, simulation was performed to a single-link mechanical system with a dynamic friction model and unknown dead zone exists at the system actuation. Then a comparison is presented with the results when there is no dead zone at the system actuation.

Keywords: Dead Zone, Nonlinear Systems, Observer, Robust Adaptive Control.

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Authors: K. Sandjak, B. 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 behavior 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 behavior 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: Nonlinear resilient behavior, unbound granular materials, RLT test results, FWD backcalculations, finite element simulations, pavement response and performance.

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Authors: Moustafa Ahmed, Ahmed Bakry, Safwat W. Z. Mahmoud

Abstract:

We model and simulate the combined effect of fiber dispersion and frequency chirp of a directly modulated high-speed laser diode on the figures of merit of a non-amplified 40-Gbps optical fiber link. We consider both the return to zero (RZ) and non-return to zero (NRZ) patterns of the pseudorandom modulation bits. The performance of the fiber communication system is assessed by the fiber-length limitation due to the fiber dispersion. We study the influence of replacing standard single-mode fibers by non-zero dispersion-shifted fibers on the maximum fiber length and evaluate the associated power penalty. We introduce new dispersion tolerances for 1-dB power penalty of the RZ and NRZ 40-Gbps optical fiber links.

Keywords: Bit error rate, dispersion, frequency chirp, fiber communications, semiconductor laser.

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Authors: C. Photiphitak, P. Rakkwamsuk, P. Muthitamongkol, C. Sae-Kung, C. Thanachayanont

Abstract:

TiO2/Ag composite films were prepared by incorporating Ag in the pores of mesoporous TiO2 films using a photoreduction method. The Ag nanoparticle sizes were in a range of 3.66-38.56 nm. The TiO2/Ag composite films were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscropy (TEM). The TiO2 films and TiO2/Ag composite films were immersed in a 0.3 mM N719 dye solution and characterized by UV-Vis spectrophotometer. The TiO2/Ag/N719 composite film showed that an optimal size of Ag nanoparticles was 19.12 nm and, hence, gave the maximum optical absorption spectra. The improved absorption was due to surface plasmon resonance induced by the Ag nanoparticles to enhance the absorption coefficient of the dye.

Keywords: Silver nanoparticle, TiO2/Ag composite films, Optical properties, surface plasmon resonance

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Authors: Yong Li

Abstract:

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.

Keywords: Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.

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Authors: M. B. Meenavathi, K. Rajesh

Abstract:

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is proposed to optimize the trade-off between noise removal and edge preservation. In this paper, we consider both the Gaussian and mixed Gaussian-impulse noise to test the robustness of the filter. Image enhancement and restoration results using the proposed Volterra filter are found to be superior to those obtained with standard linear and nonlinear filters.

Keywords: Gaussian noise, Image enhancement, Imagerestoration, Linear filters, Nonlinear filters, Volterra series.

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Authors: Sepehr Aslani, Homayoun Mahdavi-Nasab

Abstract:

Automated motion detection and tracking is a challenging task in traffic surveillance. In this paper, a system is developed to gather useful information from stationary cameras for detecting moving objects in digital videos. The moving detection and tracking system is developed based on optical flow estimation together with application and combination of various relevant computer vision and image processing techniques to enhance the process. To remove noises, median filter is used and the unwanted objects are removed by applying thresholding algorithms in morphological operations. Also the object type restrictions are set using blob analysis. The results show that the proposed system successfully detects and tracks moving objects in urban videos.

Keywords: Optical flow estimation, moving object detection, tracking, morphological operation, blob analysis.

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Authors: Barbara Kilosanidze, George Kakauridze, Levan Nadareishvili, Yuri Mshvenieradze

Abstract:

A new method for determining the distribution of birefringence and linear dichroism in optical polymer materials is presented. The method is based on the use of polarizationholographic diffraction grating that forms an orthogonal circular basis in the process of diffraction of probing laser beam on the grating. The intensities ratio of the orders of diffraction on this grating enables the value of birefringence and linear dichroism in the sample to be determined. The distribution of birefringence in the sample is determined by scanning with a circularly polarized beam with a wavelength far from the absorption band of the material. If the scanning is carried out by probing beam with the wavelength near to a maximum of the absorption band of the chromophore then the distribution of linear dichroism can be determined. An appropriate theoretical model of this method is presented. A laboratory setup was created for the proposed method. An optical scheme of the laboratory setup is presented. The results of measurement in polymer films with two-dimensional gradient distribution of birefringence and linear dichroism are discussed.

Keywords: Birefringence, graded oriented polymers, linear dichroism, optical polymers, optical anisotropy, polarization-holographic grating,

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Authors: Cemil Tunc

Abstract:

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained.

Keywords: Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

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