Search results for: order continuous norm

Authors: Olusheye Akinfenwa

Abstract:

We consider the development of an eight order Adam-s type method, with A-stability property discussed by expressing them as a one-step method in higher dimension. This makes it suitable for solving variety of initial-value problems. The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures. The methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. Numerical results obtained using the proposed block form reveals that it is highly competitive with existing methods in the literature.

Keywords: Block Adam's type Method; Periodic Ordinary Differential Equation; Stability.

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

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Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: Non-Linear Wilcoxon, robust estimation, Variogram estimation.

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Authors: Nazmona Mat Ali, Kecheng Liu

Abstract:

Knowledge is a key asset for any organisation to sustain competitive advantages, but it is difficult to identify and represent knowledge which is needed to perform activities in business processes. The effective knowledge management and support for relevant business activities definitely gives a huge impact to the performance of the organisation as a whole. This is because that knowledge have the functions of directing, coordinating and controlling actions within business processes. The study has introduced organisational morphology, a norm-based approach by applying semiotic theories which emphasise on the representation of knowledge in norms. This approach is concerned with the identification of activities into three categories: substantive, communication and control activities. All activities are directed by norms; hence three types of norms exist; each is associated to a category of activities. The paper describes the approach briefly and illustrates the application of this approach through a case study of academic activities in higher education institutions. The result of the study shows that the approach provides an effective way to profile business knowledge and the profile enables the understanding and specification of business requirements of an organisation.

Keywords: Business knowledge, Business process, Norms, Semiotics, Organisational morphology

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Authors: Mahmoud Elmezain, Ayoub Al-Hamadi, Jörg Appenrodt, Bernd Michaelis

Abstract:

Gesture recognition is a challenging task for extracting meaningful gesture from continuous hand motion. In this paper, we propose an automatic system that recognizes isolated gesture, in addition meaningful gesture from continuous hand motion for Arabic numbers from 0 to 9 in real-time based on Hidden Markov Models (HMM). In order to handle isolated gesture, HMM using Ergodic, Left-Right (LR) and Left-Right Banded (LRB) topologies is applied over the discrete vector feature that is extracted from stereo color image sequences. These topologies are considered to different number of states ranging from 3 to 10. A new system is developed to recognize the meaningful gesture based on zero-codeword detection with static velocity motion for continuous gesture. Therefore, the LRB topology in conjunction with Baum-Welch (BW) algorithm for training and forward algorithm with Viterbi path for testing presents the best performance. Experimental results show that the proposed system can successfully recognize isolated and meaningful gesture and achieve average rate recognition 98.6% and 94.29% respectively.

Keywords: Computer Vision & Image Processing, Gesture Recognition, Pattern Recognition, Application

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Authors: Rohit Gupta, Ruchika

Abstract:

In this paper, a PSO based fractional order PID (FOPID) controller is proposed for concentration control of an isothermal Continuous Stirred Tank Reactor (CSTR) problem. CSTR is used to carry out chemical reactions in industries, which possesses complex nonlinear dynamic characteristics. Particle Swarm Optimization algorithm technique, which is an evolutionary optimization technique based on the movement and intelligence of swarm is proposed for tuning of the controller for this system. Comparisons of proposed controller with conventional and fuzzy based controller illustrate the superiority of proposed PSO-FOPID controller.

Keywords: CSTR, Fractional Order PID Controller, Partical Swarm Optimization.

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Authors: Ch. Nerl, M. Wimmer, P. Hofer, E. Kaschnitz

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The present article deals with a composite casting process that allows to produce bilayer AlSn6-Al strips based on the technique of horizontal continuous casting. In the first part experimental investigations on the production of a single layer AlSn6 strip are described. Afterwards essential results of basic compound casting trials using simple test specimen are presented to define the thermal conditions required for a metallurgical compound between the alloy AlSn6 and pure aluminium. Subsequently, numerical analyses are described. A finite element model was used to examine a continuous composite casting process. As a result of the simulations the main influencing parameters concerning the thermal conditions within the composite casting region could be pointed out. Finally, basic guidance is given for the design of an appropriate composite mould system.

Keywords: Aluminium alloys, composite casting, compound casting, continuous casting, numerical simulation

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Authors: D. Kim

Abstract:

Numerical simulations are performed for laminar continuous and pulsed jets impinging on a surface in order to investigate the effects of pulsing frequency on the heat transfer characteristics. The time-averaged Nusselt number of pulsed jets is larger in the impinging jet region as compared to the continuous jet, while it is smaller in the outer wall jet region. At the stagnation point, the mean and RMS Nusselt numbers become larger and smaller, respectively, as the pulsing frequency increases. Unsteady behaviors of vortical fluid motions and temperature field are also investigated to understand the underlying mechanisms of heat transfer enhancement.

Keywords: Pulsed slot jet, impingement, pulsing frequency, heat transfer enhancement.

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Authors: V. Arbabi , I. Ebrahimzadeh, H. Ghanbari, M.M. Kaykha

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Horizontal continuous casting is widely used to produce semi-finished non-Ferrous products. Homogeneity in the metallurgical characteristics and mechanical properties for this product is vital for industrial application. In the present work, the microstructure and mechanical properties of a horizontal continuous cast two-phase brass billet have been studied. Impact strength and hardness variations were examined and the phase composition and porosity studied with image analysis software. Distinct differences in mechanical properties were observed between the upper, middle and lower parts of the billet, which are explained in terms of the morphology and size of the phase in the microstructure. Hardness variation in the length of billet is higher in upper area but impact strength is higher in lower areas.

Keywords: Horizontal Continuous Casting, Two-phase brasses, CuZn40Al1 alloy, Microstructure, Impact Strength.

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Authors: Ahmed Elrewainy

Abstract:

Mixing in the hyperspectral imaging occurs due to the low spatial resolutions of the used cameras. The existing pure materials “endmembers” in the scene share the spectra pixels with different amounts called “abundances”. Unmixing of the data cube is an important task to know the present endmembers in the cube for the analysis of these images. Unsupervised unmixing is done with no information about the given data cube. Sparsity is one of the recent approaches used in the source recovery or unmixing techniques. The l₁-norm optimization problem “basis pursuit” could be used as a sparsity-based approach to solve this unmixing problem where the endmembers is assumed to be sparse in an appropriate domain known as dictionary. This optimization problem is solved using proximal method “iterative thresholding”. The l₁-norm basis pursuit optimization problem as a sparsity-based unmixing technique was used to unmix real and synthetic hyperspectral data cubes.

Keywords: Basis pursuit, blind source separation, hyperspectral imaging, spectral unmixing, wavelets.

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Authors: T. Sakamoto, N. Hori

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A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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Authors: Yongxin Yuan

Abstract:

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D− Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.

Keywords: Model updating, iterative algorithm, gyroscopic system, partially prescribed spectral data, optimal approximation.

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Authors: A. B. Dariane, A. M. Moradi

Abstract:

A direct search approach to determine optimal reservoir operating is proposed with ant colony optimization for continuous domains (ACOR). The model is applied to a system of single reservoir to determine the optimum releases during 42 years of monthly steps. A disadvantage of ant colony based methods and the ACOR in particular, refers to great amount of computer run time consumption. In this study a highly effective procedure for decreasing run time has been developed. The results are compared to those of a GA based model.

Keywords: Ant colony optimization, continuous, metaheuristics, reservoir, decreasing run time, genetic algorithm.

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Authors: Cheng-Fang Huang, Meei-Ling Hung, Teh-Lu Liao, Her-Terng Yau, Jun-Juh Yan

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The design of chaos-based secure communication via synchronized modified Chua-s systems is investigated in this paper. A continuous control law is proposed to ensure synchronization of the master and slave modified Chua-s systems by using the variable structure control technique. Particularly, the concept of extended systems is introduced such that a continuous control input is obtained to avoid chattering phenomenon. Then, it becomes possible to ensure that the message signal embedded in the transmitter can be recovered in the receiver.

Keywords: Chaos, Secure communication, Synchronization, Variable structure control (VSC)

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Authors: Mehmet Hacibeyoglu, Ahmet Arslan, Sirzat Kahramanli

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This study analyzes the effect of discretization on classification of datasets including continuous valued features. Six datasets from UCI which containing continuous valued features are discretized with entropy-based discretization method. The performance improvement between the dataset with original features and the dataset with discretized features is compared with k-nearest neighbors, Naive Bayes, C4.5 and CN2 data mining classification algorithms. As the result the classification accuracies of the six datasets are improved averagely by 1.71% to 12.31%.

Keywords: Data mining classification algorithms, entropy-baseddiscretization method

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Authors: Raid A. Al-Aomar

Abstract:

This paper presents an application of 5S lean technology to a production facility. Due to increased demand, high product variety, and a push production system, the plant has suffered from excessive wastes, unorganized workstations, and unhealthy work environment. This has translated into increased production cost, frequent delays, and low workers morale. Under such conditions, it has become difficult, if not impossible, to implement effective continuous improvement studies. Hence, the lean project is aimed at diagnosing the production process, streamlining the workflow, removing/reducing process waste, cleaning the production environment, improving plant layout, and organizing workstations. 5S lean technology is utilized for achieving project objectives. The work was a combination of both culture changes and tangible/physical changes on the shop floor. The project has drastically changed the plant and developed the infrastructure for a successful implementation of continuous improvement as well as other best practices and quality initiatives.

Keywords: 5S Technique, Continuous Improvement, Kaizen, Lean Technology, Work Methods, Work Standards

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Authors: Abdelghani Boudiaf

Abstract:

The profusion of studies relating to the concept of organizational learning shows the importance that has been given to this concept in the management sciences. A few years ago, companies leaned towards ISO 9001 certification; this requires the implementation of the quality management system (QMS). In order for this objective to be achieved, companies must have a set of skills, which pushes them to develop learning through continuous training. The results of empirical research have shown that implementation of the QMS in the company promotes the development of learning. It should also be noted that several types of learning are developed in this sense. Given the nature of skills development is normative in the context of the quality demarche, companies are obliged to qualify and improve the skills of their human resources. Continuous training is the keystone to develop the necessary learning. To carry out continuous training, companies need to be able to identify their real needs by developing training plans based on well-defined engineering. The training process goes obviously through several stages. Initially, training has a general aspect, that is to say, it focuses on topics and actions of a general nature. Subsequently, this is done in a more targeted and more precise way to accompany the evolution of the QMS and also to make the changes decided each time (change of working method, change of practices, change of objectives, change of mentality, etc.). To answer our problematic we opted for the method of qualitative research. It should be noted that the case study method crosses several data collection techniques to explain and understand a phenomenon. Three cases of companies were studied as part of this research work using different data collection techniques related to this method.

Keywords: Changing mentalities, continuous training, organizational learning, quality management system, skills development.

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Authors: R. Parimelazhagan, N. Nagaveni

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In this paper we introduce a new class of mg-continuous mapping and studied some of its basic properties.We obtain some characterizations of such functions. Moreover we define sub minimal structure and further study certain properties of mg-closed sets.

Keywords: M-structure, mg-continuous mapping, minimal structure, mg T2 space, sub minimal structure, T12 space, mg-compact set.

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Authors: Ashu Ahuja, Shiv Narayan, Jagdish Kumar

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This paper realized the 2-DOF controller structure for first order with time delay systems. The co-prime factorization is used to design observer based controller K(s), representing one degree of freedom. The problem is based on H∞ norm of mixed sensitivity and aims to achieve stability, robustness and disturbance rejection. Then, the other degree of freedom, prefilter F(s), is formulated as fixed structure polynomial controller to meet open loop processing of reference model. This model matching problem is solved by minimizing integral square error between reference model and proposed model. The feedback controller and prefilter designs are posed as optimization problem and solved using Particle Swarm Optimization (PSO). To show the efficiency of the designed approach different variety of processes are taken and compared for analysis.

Keywords: 2-DOF, integral square error, mixed sensitivity function, observer based controller, particle swarm optimization, prefilter.

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Authors: Hoda Molavi, Sima Hoseinpoor, Hossein Bahmanyar

Abstract:

A Rotary Disc Contactor with inner diameter of 9.1cm and maximum operating height of 40cm has been used to investigate break up phenomenon. Water-Toluene, Water as continuous phase and Toluene as dispersed phase, was selected as chemical system in the experiments. The mentioned chemical system has high interfacial tension so it was possible to form big drops which permit accurate investigation on break up phenomenon as well as the first and second critical rotor speeds. In this study, Break up phenomenon has been studied as a function of mother drop size, rotor speed and continuous phase height. Further more; the effects of mother drop size and continuous phase height on the first and second critical rotor speeds were investigated. Finally, two modified correlations were proposed to estimate the first and second critical speeds.

Keywords: Breakage, First critical rotor speed, Rotary disccontactor, Second critical rotor speed

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: Afshin Ahmadi Nadooshan, Ebrahim Shirani

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In this paper, the two-dimensional stagger grid interface pressure (SGIP) model has been generalized and presented into three-dimensional form. For this purpose, various models of surface tension force for interfacial flows have been investigated and compared with each other. The VOF method has been used for tracking the interface. To show the ability of the SGIP model for three-dimensional flows in comparison with other models, pressure contours, maximum spurious velocities, norm spurious flow velocities and pressure jump error for motionless drop of liquid and bubble of gas are calculated using different models. It has been pointed out that SGIP model in comparison with the CSF, CSS and PCIL models produces the least maximum and norm spurious velocities. Additionally, the new model produces more accurate results in calculating the pressure jumps across the interface for motionless drop of liquid and bubble of gas which is generated in surface tension force.

Keywords: Volume-of-Fluid; SGIP model; CSS model; CSF model; PCIL model; surface tension force; spurious currents.

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Authors: Mahdi Sharifian, Mohammad Ali Fanaei

Abstract:

Saccharomyces cerevisiae (baker-s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance models can be used to capture the dynamic behavior of such cultures. In this paper an unstructured, segregated model is used which is based on population balance equation(PBE) and then in order to simulation, the 4th order Rung-Kutta is used for time dimension and three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used for discretization of the cell mass domain. The results indicate that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results show that although the PI controller has simpler structure, the GLC has better performance.

Keywords: Bioreactor, cell population balance, finite difference, orthogonal collocation on finite elements, Galerkin finite element, feedback linearization, PI controller.

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Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

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The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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Authors: Jinfeng Wang, Yuanhong Bi, Hong Li, Yang Liu, Meng Zhao

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In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L1( ¯ J,L2( )-norm are obtained.

Keywords: Convection-dominated diffusion equation, expanded mixed method, time discontinuous scheme, stability, error estimates.

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Authors: L. Gaile, I. Radinsh

Abstract:

Based on experimental data using accelerometry technology there was developed an analytical model that approximates human induced ground reaction forces in vertical, longitudinal and lateral directions ascending and descending the stairs. Proposed dynamic loading factors and corresponding phase shifts for the first five harmonics of continuous walking force history in case of stair ascend and descend. Into account is taken imperfectness of individual footfall forcing functions, differences between continuous walking force histories among individuals. There is proposed mean synthetic continuous walking force history that can be used in numerical simulations of human movement on the stairs.

Keywords: footfall, ground reaction forces, human loads, serviceability, stair vibration, walking

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Authors: Ane Larrea, Victor Sebastian, Manuel Arruebo, Jesus Santamaria

Abstract:

We present a gas-liquid microfluidic system as a reactor to obtain magnetite nanoparticles with an excellent degree of control regarding their crystalline phase, shape and size. Several types of microflow approaches were selected to prevent nanomaterial aggregation and to promote homogenous size distribution. The selected reactor consists of a mixer stage aided by ultrasound waves and a reaction stage using a N2-liquid segmented flow to prevent magnetite oxidation to non-magnetic phases. A milli-fluidic reactor was developed to increase the production rate where a magnetite throughput close to 450 mg/h in a continuous fashion was obtained.

Keywords: Microfluidics, magnetic nanoparticles, continuous production, nanomaterials.

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

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Reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM), using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Mihailov stability criterion and continued fraction expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. In the evolutionary technique method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.

Keywords: Reduced Order Modeling, Stability, Continued Fraction Expansions, Mihailov Stability Criterion, Particle Swarm Optimization, Integral Squared Error.

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Authors: Karel Borovec, Jerzy Gorecki, Tadeas Ochodek

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Combustion of solid fuels is one of the main sources of mercury in the environment. To reduce the amount of mercury emitted to the atmosphere, it is necessary to modify or optimize old purification technologies or introduce the new ones. Effective reduction of mercury level in the flue gas requires the use of speciation systems for mercury form determination. This paper describes tests and provides comparison of two industrial portable and continuous systems for mercury speciation in the flue gas: Durag HM-1400 TRX with a speciation module and the Portable Continuous Mercury Speciation System based on the SGM-8 mercury speciation set, made by Nippon Instruments Corporation. Additionally, the paper describes a few analytical problems that were encountered during a two-year period of using the systems.

Keywords: Mercury determination, speciation, continuous measurement, flue gas.

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Authors: Raja Muhammad Asif Zahoor, Junaid Ali Khan, I. M. Qureshi

Abstract:

In this article an evolutionary technique has been used for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been successfully applied to solve the different forms of Riccati differential equations. The strength of proposed method has in its equal applicability for the integer order case, as well as, fractional order case. Comparison of the method has been made with standard numerical techniques as well as the analytic solutions. It is found that the designed method can provide the solution to the equation with better accuracy than its counterpart deterministic approaches. Another advantage of the given approach is to provide results on entire finite continuous domain unlike other numerical methods which provide solutions only on discrete grid of points.

Keywords: Riccati Equation, Non linear ODE, Fractional differential equation, Genetic algorithm.

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Authors: Anders Schou Simonsen, Thomas Condra, Kim Sørensen

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Various processes are modelled using a discrete phase, where particles are seeded from a source. Such particles can represent liquid water droplets, which are affecting the continuous phase by exchanging thermal energy, momentum, species etc. Discrete phases are typically modelled using parcel, which represents a collection of particles, which share properties such as temperature, velocity etc. When coupling the phases, the exchange rates are integrated over the cell, in which the parcel is located. This can cause spikes and fluctuating exchange rates. This paper presents an alternative method of coupling a discrete and a continuous plug flow phase. This is done using triangular parcels, which span between nodes following the dynamics of single droplets. Thus, the triangular parcels are propagated using the corner nodes. At each time step, the exchange rates are spatially integrated over the surface of the triangular parcels, which yields a smooth continuous exchange rate to the continuous phase. The results shows that the method is more stable, converges slightly faster and yields smooth exchange rates compared with the steam tube approach. However, the computational requirements are about five times greater, so the applicability of the alternative method should be limited to processes, where the exchange rates are important. The overall balances of the exchanged properties did not change significantly using the new approach.

Keywords: CFD, coupling, discrete phase, parcel.

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