Search results for: Linear Optical Scanner
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2399

Search results for: Linear Optical Scanner

2039 Identification of Nonlinear Systems Structured by Hammerstein-Wiener Model

Authors: A. Brouri, F. Giri, A. Mkhida, F. Z. Chaoui, A. Elkarkri, M. L. Chhibat

Abstract:

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.

Keywords: Nonlinear system identification, Hammerstein systems, Wiener systems, frequency identification.

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2038 Numerical Simulations on Feasibility of Stochastic Model Predictive Control for Linear Discrete-Time Systems with Random Dither Quantization

Authors: Taiki Baba, Tomoaki Hashimoto

Abstract:

The random dither quantization method enables us to achieve much better performance than the simple uniform quantization method for the design of quantized control systems. Motivated by this fact, the stochastic model predictive control method in which a performance index is minimized subject to probabilistic constraints imposed on the state variables of systems has been proposed for linear feedback control systems with random dither quantization. In other words, a method for solving optimal control problems subject to probabilistic state constraints for linear discrete-time control systems with random dither quantization has been already established. To our best knowledge, however, the feasibility of such a kind of optimal control problems has not yet been studied. Our objective in this paper is to investigate the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. To this end, we provide the results of numerical simulations that verify the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization.

Keywords: Model predictive control, stochastic systems, probabilistic constraints, random dither quantization.

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2037 Optical Induction of 2D and 3D Photonic Lattices in Photorefractive Materials based on Talbot effect

Authors: A. Badalyan, R. Hovsepyan, V. Mekhitaryan, P. Mantashyan, R. Drampyan

Abstract:

In this paper we report the technique of optical induction of 2 and 3-dimensional (2D and 3D) photonic lattices in photorefractive materials based on diffraction grating self replication -Talbot effect. 1D and 2D different rotational symmery diffraction masks with the periods of few tens micrometers and 532 nm cw laser beam were used in the experiments to form an intensity modulated light beam profile. A few hundred micrometric scale replications of mask generated intensity structures along the beam propagation axis were observed. Up to 20 high contrast replications were detected for 1D annular mask with 30

Keywords: Diffraction gratings, laser, photonic lattice, Talbot effect.

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2036 Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach

Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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2035 An Improved Prediction Model of Ozone Concentration Time Series Based On Chaotic Approach

Authors: N. Z. A. Hamid, M. S. M. Noorani

Abstract:

This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly Ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: Chaotic approach, phase space, Cao method, local linear approximation method.

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2034 Takagi-Sugeno Fuzzy Control of Induction Motor

Authors: Allouche Moez, Souissi Mansour, Chaabane Mohamed, Mehdi Driss

Abstract:

This paper deals with the synthesis of fuzzy state feedback controller of induction motor with optimal performance. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a non linear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy controller is designed to stabilise the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The gains of fuzzy control are obtained by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results are given to demonstrate the controller-s effectiveness.

Keywords: Rejection disturbance, fuzzy modelling, open-loop control, Fuzzy feedback controller, fuzzy observer, Linear Matrix Inequality (LMI)

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2033 Study of a Fabry-Perot Resonator

Authors: F. Hadjaj, A. Belghachi, A. Halmaoui, M. Belhadj, H. Mazouz

Abstract:

A laser is essentially an optical oscillator consisting of a resonant cavity, an amplifying medium and a pumping source. In semiconductor diode lasers, the cavity is created by the boundary between the cleaved face of the semiconductor crystal and air, and has reflective properties as a result of the differing refractive indices of the two media. For a GaAs-air interface a reflectance of 0.3 is typical and therefore the length of the semiconductor junction forms the resonant cavity. To prevent light being emitted in unwanted directions from the junction, sides perpendicular to the required direction are roughened. The objective of this work is to simulate the optical resonator Fabry-Perot and explore its main characteristics, such as FSR, finesse, linewidth, transmission and so on, that describe the performance of resonator.

Keywords: Fabry-Perot Resonator, laser diode.

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2032 Traction Behavior of Linear Piezo-Viscous Lubricants in Rough Elastohydrodynamic Lubrication Contacts

Authors: Punit Kumar, Niraj Kumar

Abstract:

The traction behavior of lubricants with the linear pressure-viscosity response in EHL line contacts is investigated numerically for smooth as well as rough surfaces. The analysis involves the simultaneous solution of Reynolds, elasticity and energy equations along with the computation of lubricant properties and surface temperatures. The temperature modified Doolittle-Tait equations are used to calculate viscosity and density as functions of fluid pressure and temperature, while Carreau model is used to describe the lubricant rheology. The surface roughness is assumed to be sinusoidal and it is present on the nearly stationary surface in near-pure sliding EHL conjunction. The linear P-V oil is found to yield much lower traction coefficients and slightly thicker EHL films as compared to the synthetic oil for a given set of dimensionless speed and load parameters. Besides, the increase in traction coefficient attributed to surface roughness is much lower for the former case. The present analysis emphasizes the importance of employing realistic pressure-viscosity response for accurate prediction of EHL traction.

Keywords: EHL, linear pressure-viscosity, surface roughness, traction, water/glycol.

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2031 Improved Asymptotic Stability Analysis for Lure Systems with Neutral Type and Time-varying Delays

Authors: Changchun Shen, Shouming Zhong

Abstract:

This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Lur'e system, linear matrix inequalities, Lyapunov, stability.

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2030 Linear-Operator Formalism in the Analysis of Omega Planar Layered Waveguides

Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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2029 Fiber Optic Sensors

Authors: Bahareh Gholamzadeh, Hooman Nabovati

Abstract:

Fiber optic sensor technology offers the possibility of sensing different parameters like strain, temperature, pressure in harsh environment and remote locations. these kinds of sensors modulates some features of the light wave in an optical fiber such an intensity and phase or use optical fiber as a medium for transmitting the measurement information. The advantages of fiber optic sensors in contrast to conventional electrical ones make them popular in different applications and now a day they consider as a key component in improving industrial processes, quality control systems, medical diagnostics, and preventing and controlling general process abnormalities. This paper is an introduction to fiber optic sensor technology and some of the applications that make this branch of optic technology, which is still in its early infancy, an interesting field.

Keywords: Fiber optic sensors, distributed sensors, sensorapplication, crack sensor.

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2028 Harmonics Elimination in Multilevel Inverter Using Linear Fuzzy Regression

Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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2027 Sol-gel Synthesis and Optical Characterisation of TiO2 Thin Films for Photovoltaic Application

Authors: N. H. Arabi, Aicha Iratni, Talaighil Razika, Bruno Capoen, Mohamed Bouazaoui

Abstract:

TiO2 thin films have been prepared by the sol-gel dipcoating technique in order to elaborate antireflective thin films for monocrystalline silicon (mono-Si). The titanium isopropoxyde was chosen as a precursor with hydrochloric acid as a catalyser for preparing a stable solution. The optical properties have been tailored with varying the solution concentration, the withdrawn speed, and the heat-treatment. We showed that using a TiO2 single layer with 64.5 nm in thickness, heat-treated at 450°C or 300°C reduces the mono-Si reflection at a level lower than 3% over the broadband spectral domains [669-834] nm and [786-1006] nm respectively. Those latter performances are similar to the ones obtained with double layers of low and high refractive index glasses respectively.

Keywords: Dip coating, mono-Si, titanium oxide, thin film.

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2026 High Energy Dual-Wavelength Mid-Infrared Extracavity KTA Optical Parametric Oscillator

Authors: Hongjun Liu, Qibing Sun, Nan Huang, Shaolan Zhu, Wei Zhao

Abstract:

A high energy dual-wavelength extracavity KTA optical parametric oscillator (OPO) with excellent stability and beam quality, which is pumped by a Q-switched single-longitudinal-mode Nd:YAG laser, has been demonstrated based on a type II noncritical phase matching (NCPM) KTA crystal. The maximum pulse energy of 10.2 mJ with the output stability of better than 4.1% rms at 3.467 μm is obtained at the repetition rate of 10 Hz and pulse width of 2 ns, and the 11.9 mJ of 1.535 μm radiation is obtained simultaneously. This extracavity NCPM KTA OPO is very useful when high energy, high beam quality and smooth time domain are needed.

Keywords: mid-infrared laser, OPO, dual-wavelength laser

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2025 A Novel Optimal Setting for Directional over Current Relay Coordination using Particle Swarm Optimization

Authors: D. Vijayakumar, R. K. Nema

Abstract:

Over Current Relays (OCRs) and Directional Over Current Relays (DOCRs) are widely used for the radial protection and ring sub transmission protection systems and for distribution systems. All previous work formulates the DOCR coordination problem either as a Non-Linear Programming (NLP) for TDS and Ip or as a Linear Programming (LP) for TDS using recently a social behavior (Particle Swarm Optimization techniques) introduced to the work. In this paper, a Modified Particle Swarm Optimization (MPSO) technique is discussed for the optimal settings of DOCRs in power systems as a Non-Linear Programming problem for finding Ip values of the relays and for finding the TDS setting as a linear programming problem. The calculation of the Time Dial Setting (TDS) and the pickup current (Ip) setting of the relays is the core of the coordination study. PSO technique is considered as realistic and powerful solution schemes to obtain the global or quasi global optimum in optimization problem.

Keywords: Directional over current relays, Optimization techniques, Particle swarm optimization, Power system protection.

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2024 Controller Synthesis of Switched Positive Systems with Bounded Time-Varying Delays

Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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2023 Solution of Fuzzy Maximal Flow Problems Using Fuzzy Linear Programming

Authors: Amit Kumar, Manjot Kaur

Abstract:

In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

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2022 Statistical Evaluation of Nonlinear Distortion using the Multi-Canonical Monte Carlo Method and the Split Step Fourier Method

Authors: Ioannis Neokosmidis, Nikos Gkekas, Thomas Kamalakis, Thomas Sphicopoulos

Abstract:

In high powered dense wavelength division multiplexed (WDM) systems with low chromatic dispersion, four-wave mixing (FWM) can prove to be a major source of noise. The MultiCanonical Monte Carlo Method (MCMC) and the Split Step Fourier Method (SSFM) are combined to accurately evaluate the probability density function of the decision variable of a receiver, limited by FWM. The combination of the two methods leads to more accurate results, and offers the possibility of adding other optical noises such as the Amplified Spontaneous Emission (ASE) noise.

Keywords: Monte Carlo, Nonlinear optics, optical crosstalk, Wavelength-division Multiplexing (WDM).

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2021 Effective Design Parameters on the End Effect in Single-Sided Linear Induction Motors

Authors: A. Zare Bazghaleh, M. R. Naghashan, H. Mahmoudimanesh, M. R. Meshkatoddini

Abstract:

Linear induction motors are used in various industries but they have some specific phenomena which are the causes for some problems. The most important phenomenon is called end effect. End effect decreases efficiency, power factor and output force and unbalances the phase currents. This phenomenon is more important in medium and high speeds machines. In this paper a factor, EEF , is obtained by an accurate equivalent circuit model, to determine the end effect intensity. In this way, all of effective design parameters on end effect is described. Accuracy of this equivalent circuit model is evaluated by two dimensional finite-element analysis using ANSYS. The results show the accuracy of the equivalent circuit model.

Keywords: Linear induction motor, end effect, equivalent circuitmodel, finite-element method.

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2020 Order Reduction by Least-Squares Methods about General Point ''a''

Authors: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

Abstract:

The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

Keywords: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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2019 System of Programs for Rapid Development and Execution of Palm OS Applications

Authors: Mihai Ciocarlie, Marcela-Simona Atanasoae, Horia Ciocarlie

Abstract:

We present the development of a system of programs designed for the compilation and execution of applications for handheld computers. In introduction we describe the purpose of the project and its components. The next two paragraphs present the first two components of the project (the scanner and parser generators). Then we describe the Object Pascal compiler and the virtual machines for Windows and Palm OS. In conclusion we emphasize the ways in which the project can be extended.

Keywords: Compiler design, Palm OS applications, rapid application development, virtual machine.

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2018 Optimal Control Strategies for Speed Control of Permanent-Magnet Synchronous Motor Drives

Authors: Roozbeh Molavi, Davood A. Khaburi

Abstract:

The permanent magnet synchronous motor (PMSM) is very useful in many applications. Vector control of PMSM is popular kind of its control. In this paper, at first an optimal vector control for PMSM is designed and then results are compared with conventional vector control. Then, it is assumed that the measurements are noisy and linear quadratic Gaussian (LQG) methodology is used to filter the noises. The results of noisy optimal vector control and filtered optimal vector control are compared to each other. Nonlinearity of PMSM and existence of inverter in its control circuit caused that the system is nonlinear and time-variant. With deriving average model, the system is changed to nonlinear time-invariant and then the nonlinear system is converted to linear system by linearization of model around average values. This model is used to optimize vector control then two optimal vector controls are compared to each other. Simulation results show that the performance and robustness to noise of the control system has been highly improved.

Keywords: Kalman filter, Linear quadratic Gaussian (LQG), Linear quadratic regulator (LQR), Permanent-Magnet synchronousmotor (PMSM).

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2017 Computational Aspects of Regression Analysis of Interval Data

Authors: Michal Cerny

Abstract:

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

Keywords: Linear regression, interval-censored data, computational complexity.

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2016 New Adaptive Linear Discriminante Analysis for Face Recognition with SVM

Authors: Mehdi Ghayoumi

Abstract:

We have applied new accelerated algorithm for linear discriminate analysis (LDA) in face recognition with support vector machine. The new algorithm has the advantage of optimal selection of the step size. The gradient descent method and new algorithm has been implemented in software and evaluated on the Yale face database B. The eigenfaces of these approaches have been used to training a KNN. Recognition rate with new algorithm is compared with gradient.

Keywords: lda, adaptive, svm, face recognition.

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2015 The Rail Traffic Management with Usage of C-OTDR Monitoring Systems

Authors: Andrey V. Timofeev, Dmitry V. Egorov, Viktor M. Denisov

Abstract:

This paper presents development results of usage of C-OTDR monitoring systems for rail traffic management. The COTDR method is based on 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 source positions and to identify their types. This approach proved successful for rail traffic management (moving block system, weigh- in-motion system etc.).

Keywords: C-OTDR systems, moving block-sections, rail traffic management, Rayleigh backscattering, weigh-in-motion.

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2014 A Fuzzy Linear Regression Model Based on Dissemblance Index

Authors: Shih-Pin Chen, Shih-Syuan You

Abstract:

Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: Dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming.

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2013 Effect of Fire Retardant Painting Product on Smoke Optical Density of Burning Natural Wood Samples

Authors: Abdullah N. Olimat, Ahmad S. Awad, Faisal M. AL-Ghathian

Abstract:

Natural wood is used in many applications in Jordan such as furniture, partitions constructions, and cupboards. Experimental work for smoke produced by the combustion of certain wood samples was studied. Smoke generated from burning of natural wood, is considered as a major cause of death in furniture fires. The critical parameter for life safety in fires is the available time for escape, so the visual obscuration due to smoke release during fire is taken into consideration. The effect of smoke, produced by burning of wood, depends on the amount of smoke released in case of fire. The amount of smoke production, apparently, affects the time available for the occupants to escape. To achieve the protection of life of building occupants during fire growth, fire retardant painting products are tested. The tested samples of natural wood include Beech, Ash, Beech Pine, and white Beech Pine. A smoke density chamber manufactured by fire testing technology has been used to perform measurement of smoke properties. The procedure of test was carried out according to the ISO-5659. A nonflammable vertical radiant heat flux of 25 kW/m2 is exposed to the wood samples in a horizontal orientation. The main objective of the current study is to carry out the experimental tests for samples of natural woods to evaluate the capability to escape in case of fire and the fire safety requirements. Specific optical density, transmittance, thermal conductivity, and mass loss are main measured parameters. Also, comparisons between samples with paint and with no paint are carried out between the selected samples of woods.

Keywords: Optical density, specific optical density, transmittance, visibility.

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2012 Modeling Bessel Beams and Their Discrete Superpositions from the Generalized Lorenz-Mie Theory to Calculate Optical Forces over Spherical Dielectric Particles

Authors: Leonardo A. Ambrosio, Carlos. H. Silva Santos, Ivan E. L. Rodrigues, Ayumi K. de Campos, Leandro A. Machado

Abstract:

In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables.

Keywords: Bessel Beams and Frozen Waves, Generalized Lorenz-Mie Theory, Numerical Methods, Optical Forces.

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2011 A Novel Method for Areal Surface Roughness Measurement

Authors: Romuald Synak, Wlodzimierz Lipinski, Marcin Pawelczak

Abstract:

An area-integrating method that uses the technique of total integrated light scatter for evaluating the root mean square height of the surface Sq has been presented in the paper. It is based on the measurement of the scatter power using a flat photodiode integrator rather than an optical sphere or a hemisphere. By this means, one can obtain much less expensive and smaller instruments than traditional ones. Thanks to this, they could find their application for surface control purposes, particularly in small and medium size enterprises. A description of the functioning of the measuring unit as well as the impact caused by different factors on its properties is presented first. Next, results of measurements of the Sq values performed for optical, silicon and metal samples have been shown. It has been also proven that they are in a good agreement with the results obtained using the Ulbricht sphere instrument.

Keywords: ISO 25178 Standard, scatterometry, surface metrology, surface roughness

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2010 On the Sphere Method of Linear Programming Using Multiple Interior Points Approach

Authors: Job H. Domingo, Carolina Bancayrin-Baguio

Abstract:

The Sphere Method is a flexible interior point algorithm for linear programming problems. This was developed mainly by Professor Katta G. Murty. It consists of two steps, the centering step and the descent step. The centering step is the most expensive part of the algorithm. In this centering step we proposed some improvements such as introducing two or more initial feasible solutions as we solve for the more favorable new solution by objective value while working with the rigorous updates of the feasible region along with some ideas integrated in the descent step. An illustration is given confirming the advantage of using the proposed procedure.

Keywords: Interior point, linear programming, sphere method, initial feasible solution, feasible region, centering and descent steps, optimal solution.

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