Search results for: fractional crystallization

Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Christina Roman, Deepak Koirala, Joseph A. Piccirilli

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Phage displaying synthetic Fab libraries have been used to obtain Fabs that bind to specific RNA targets with high affinity and specificity. These Fabs have been demonstrated to facilitate RNA crystallization. However, the antibody framework used in the construction of these phage display libraries contains numerous bulky, flexible, and charged residues, which facilitate solubility and hinder aggregation. These residues can interfere with crystallization due to the entropic cost associated with burying them within crystal contacts. To systematically reduce the surface entropy of the Fabs and improve their crystallization properties, a protein engineering strategy termed surface entropy reduction (SER) is being applied to the Fab framework. In this approach, high entropy residues are mutated to smaller ones such as alanine or serine. Focusing initially on Fab BL3-6, which binds an RNA AAACA pentaloop with 20nM affinity, the SER P server (http://services.mbi.ucla.edu/SER/) was used and analysis was performed on existing RNA-Fab BL3-6 co-crystal structures. From this analysis twelve surface entropy reduced mutants were designed. These SER mutants were expressed and are now being measured for their crystallization and diffraction performance with various RNA targets. So far, one mutant has generated 3.02 angstrom diffraction with the yjdF riboswitch RNA. Ultimately, the most productive mutations will be combined into a new Fab framework to be used in a optimized phage displayed Fab library.

Keywords: antibody fragment, crystallography, RNA, surface entropy reduction

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: Bright Kwakye-Awuah, Elizabeth Von-Kiti, Isaac Nkrumah, Baah Sefa-Ntiri, Craig D. Williams

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Bauxite and kaolin from Ghana Bauxite Company mine site were used to synthesize zeolites. Bauxite served as the alumina source and kaolin the silica source. Synthesis variations include variation of aging time at constant crystallization time and variation of crystallization times at constant aging time. Characterization techniques such as X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive x-ray analysis (EDX) and Fourier transform infrared spectroscopy (FTIR) were employed in the characterization of the raw samples as well as the synthesized samples. The results obtained showed that the transformations that occurred and the phase of the resulting products were coordinated by the aging time, crystallization time, alkaline concentration and Si/Al ratio of the system. Zeolites A, X, Y, analcime, Sodalite, and ZK-14 were some of the phases achieved. Zeolite LTA was achieved with short crystallization times of 3, 5, 18 and 24 hours and a maximum aging of 24 hours. Zeolite LSX was synthesized with 24 hr aging followed with 24 hr hydrothermal treatment whilst zeolite Y crystallized after 48 hr of aging and 24 hr crystallization. Prolonged crystallization time produced a mixed phased product. Prolonged aging times, on the other hand, did not yield any zeolite as the sample was amorphous. Increasing the alkaline content of the reaction mixture above 5M introduced sodalite phase in the final product. The properties of the final products were comparable to zeolites synthesized from pure chemical reagents.

Keywords: bauxite, kaolin, aging, crystallization, zeolites

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Authors: A. Cherifi, B. Bouazza, A. O. Dahmane, B. Yagoubi

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Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed.

Keywords: OFDM, (FrFT) fractional fourier transform, optical OFDM, equalization algorithm

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Authors: Neelam Singha

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The present work intends to analyze the system dynamics of Hashimoto’s thyroiditis with the assistance of fractional calculus. Hashimoto’s thyroiditis or chronic lymphocytic thyroiditis is an autoimmune disorder in which the immune system attacks the thyroid gland, which gradually results in interrupting the normal thyroid operation. Consequently, the feedback control of the system gets disrupted due to thyroid follicle cell lysis. And, the patient perceives life-threatening clinical conditions like goiter, hyperactivity, euthyroidism, hyperthyroidism, etc. In this work, we aim to obtain the approximate solution to the posed fractional-order problem describing Hashimoto’s thyroiditis. We employ the Adomian decomposition method to solve the system of fractional-order differential equations, and the solutions obtained shall be useful to provide information about the effect of medical care. The numerical technique is executed in an organized manner to furnish the associated details of the progression of the disease and to visualize it graphically with suitable plots.

Keywords: adomian decomposition method, fractional derivatives, Hashimoto's thyroiditis, mathematical modeling

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Authors: Harendra Singh, Rajesh Pandey

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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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Authors: Golden J. Zhang, Dongbao Zhou

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Darcy’s law is the fundamental theory in fluid dynamics and engineering applications. Although Darcy linearity was found to be valid for slow, viscous flow, non-linear and non-Darcian flow has been well documented under both small and large velocity fluid flow. Various classical models were proposed and used widely to quantify non-Darcian flow, including the well-known Forchheimer, Izbash, and Swartzendruber models. Applications, however, revealed limitations of these models. Here we propose a general model built upon the Caputo fractional derivative to quantify non-Darcian flow for various flows (laminar to turbulence).Real-world applications and model comparisons showed that the new fractional-derivative model, which extends the fractional model proposed recently by Zhou and Yang (2018), can capture the non-Darcian flow in the relatively small velocity in low-permeability deposits and the relatively high velocity in high-permeability sand. A scale effect was also identified for non-Darcian flow in fractured rocks. Therefore, fractional calculus may provide an efficient tool to improve classical models to quantify fluid dynamics in aquatic environments.

Keywords: fractional derivative, darcy’s law, non-darcian flow, fluid dynamics

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Authors: Anand Kishore Kola, G. Uday Bhaskar Babu, Kotturi Ajay Kumar

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The modern dynamic systems used in industries are complex in nature and hence the fractional order controllers have been contemplated as a fresh approach to control system design that takes the complexity into account. Traditional integer order controllers use integer derivatives and integrals to control systems, whereas fractional order controllers use fractional derivatives and integrals to regulate memory and non-local behavior. This study provides a method based on the maximumsensitivity (Ms) methodology to discover all resilient fractional filter Internal Model Control - proportional integral derivative (IMC-PID) controllers that stabilize the closed-loop system and deliver the highest performance for a time delay system with a Smith predictor configuration. Additionally, it helps to enhance the range of PID controllers that are used to stabilize the system. This study also evaluates the effectiveness of the suggested controller approach for minimum phase system in comparison to those currently in use which are based on Integral of Absolute Error (IAE) and Total Variation (TV).

Keywords: modern dynamic systems, fractional order controllers, maximum-sensitivity, IMC-PID controllers, Smith predictor, IAE and TV

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Authors: Ali Afaghi, Sehraneh Ghaemi

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The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.

Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs

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Authors: B. F. Nteumagne, E. Pindza, E. Mare

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We apply Lie symmetries analysis to price and hedge options in the fractional Brownian framework. The reputation of Lie groups is well spread in the area of Mathematical sciences and lately, in Finance. In the presence of transactions costs and under fractional Brownian motions, analytical solutions become difficult to obtain. Lie symmetries analysis allows us to simplify the problem and obtain new analytical solution. In this paper, we investigate the use of symmetries to reduce the partial differential equation obtained and obtain the analytical solution. We then proposed a hedging procedure and calibration technique for these types of options, and test the model on real market data. We show the robustness of our methodology by its application to the pricing of digital options.

Keywords: fractional brownian model, symmetry, transaction cost, option pricing

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Authors: Pixiang Wang, Shaoyang Liu, Yucheng Peng

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Polypropylene (PP) is an essential material of numerous applications in different industrial sectors, including packaging, construction, and automotive. Because the application of homopolypropylene (HPP) is limited by its relatively low impact strength and high embrittlement temperature, various types of impact copolymer PP (ICPP) that incorporate elastomers/rubbers into HPP to increase impact strength have been successfully commercialized. Crystallization kinetics of an isotactic HPP, an ICPP, and their composites were studied in this work understand the composites’ behaviors better. The Avrami-Jeziorny model was used to describe the crystallization process. For most samples, the Avrami exponent, n, was greater than 3, indicating the crystal grew in three dimensions with spherical geometry. However, the n value could drop below 3 when the ICPP content was 80 wt.% or higher and the cooling rate was 7.5°C/min or lower, implying that the crystals could grow in two dimensions and some lamella structures could be formed under those conditions. The nucleation activity increased with the increase of the ICPP content, demonstrating that the rubber phase in the ICPP acted as a nucleation agent and facilitated the nucleation process. The decrease in crystallization rate after the ICPP content exceeded 60 wt.% might be caused by the excessive amount of crystal nuclei induced by the high ICPP content, which caused strong crystal-crystal interactions and limited the crystal growth space. The nucleation activity and the n value showed high correlations to the mechanical and thermal properties of the materials. The quantitative study of the kinetics of crystallization in this work could be a helpful reference for manufacturing ICPP and HPP/ICPP mixtures.

Keywords: polypropylene, crystallization kinetics, Avrami-Jeziorny model, crystallization activation energy, Nucleation activity

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Marcin Sowa

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The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: numerical method, SubIval, fractional calculus, numerical solver, circuit analysis

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Authors: Jianwei Ma, Diriba Gemechu

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In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.

Keywords: anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, split Bregman algorithm

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: Zehui Du, Chaiwat Prapainainar, Paisan Kongkachuichay, Paweena Prapainainar

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The aim of this work was to obtain small crystalline size and high crystallinity of mordenites and analcimes, by modifying the aging time, agitation, water content, crystallization temperature and crystallization time. Two different hydrothermal methods were studied. Both methods used Na2SiO3 as the silica source, NaAlO2 as the aluminum source, and NaOH as the alkali source. The first method used HMI as the template while the second method did not use the template. Mordenite crystals with spherical shape and bimodal in size of about 1 and 5 µm were obtained from the first method using conditions of 24 hr aging time, 170°C and 24 hr crystallization. Modernites with high crystallinity were formed using agitation system in the crystallization process. It was also found that the aging time of 2 hr and 24 hr did not much affect the formation of mordenite crystals. Analcime crystals were formed in spherical shape and facet on surface with the size between 13-15 µm by the second method using the conditions of 30 minutes aging time, 170°C and 24 hr crystallization without calcination. By increasing water content, the crystallization process was slowed down and resulted in smaller analcime crystals. Larger size of analcime crystals were observed when the samples were calcined at 300°C and 580°C. Higher calcination temperature led to higher crystal growth and resulted in larger crystal size. Finally, mordenite and analcime was used as fillers in zeolite/Nafion composite membrane to solve the fuel cross over problem in direct alcohol fuel cell.

Keywords: analcime, hydrothermal synthesis, mordenite, zeolite

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Authors: Jong-Jy Shyu, Soo-Chang Pei, Yun-Da Huang

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In this paper, design of wide-range variable fractional-delay (WR-VFD) finite impulse response (FIR) digital filters is proposed. With respect to the conventional VFD filter which is designed such that its delay is adjustable within one unit, the proposed VFD FIR filter is designed such that its delay can be tunable within a wider range. By the traces of coefficients of the fractional-delay FIR filter, it is found that the conventional method of polynomial substitution for filter coefficients no longer satisfies the design demand, and the circuits perform the sinc function (sinc converter) are added to overcome this problem. In this paper, least-squares method is adopted to design WR-VFD FIR filter. Throughout this paper, several examples will be proposed to demonstrate the effectiveness of the presented methods.

Keywords: digital filter, FIR filter, variable fractional-delay (VFD) filter, least-squares approximation

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Authors: Amirali Ebrahimi, T. A. G. Langrish

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The effect of various humidities on process yields and degrees of crystallinity for spray-dried powders from spray drying of lactose with humid air in a straight-through system have been studied. It has been suggested by Williams–Landel–Ferry kinetics (WLF) that a higher particle temperature and lower glass-transition temperature would increase the crystallization rate of the particles during the spray-drying process. Freshly humidified air produced by a Buchi-B290 spray dryer as a humidifier attached to the main spray dryer decreased the particle glass-transition temperature (Tg), while allowing the particle temperature (Tp) to reach higher values by using an insulated drying chamber. Differential scanning calorimetry (DSC) and moisture sorption analysis were used to measure the degree of crystallinity for the spray-dried lactose powders. The results showed that higher Tp-Tg, as a result of applying humid air, improved the process yield from 21 ± 4 to 26 ± 2% and crystallinity of the particles by decreasing the latent heat of crystallization from 43 ± 1 to 30 ± 11 J/g and the sorption peak height from 7.3 ± 0.7% to 6 ± 0.7%.

Keywords: lactose, crystallization, spray drying, humid air

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Authors: Fouzi Aboura

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The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s.

Keywords: FOPID controller, fractional order, AVR system, objective function, optimization, GA, PSO, HGAPSO

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Authors: Rabindranath Jana, Plabani Basu, Keka Rana

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Nucleating agents are widely used to modify the properties of various polymers. The rate of crystallization and the size of the crystals have a strong impact on mechanical and optical properties of a polymer. The addition of nucleating agents to the semi-crystalline polymers provides a surface on which the crystal growth can start easily. As a consequence, fast crystal formation will result in many small crystal domains so that the cycle times for injection molding may be reduced. Moreover, the mechanical properties e.g., modulus, tensile strength, heat distortion temperature and hardness may increase. In the present work, multi-walled carbon nanotubes (MWNTs) as nucleating agents for the crystallization of poly (e-caprolactone)diol (PCL). Thus nanocomposites of PCL filled with MWNTs were prepared by solution blending. Differential scanning calorimetry (DSC) tests were carried out to study the effect of CNTs on on-isothermal crystallization of PCL. The polarizing optical microscopy (POM), and wide-angle X-ray diffraction (WAXD) were used to study the morphology and crystal structure of PCL and its nanocomposites. It is found that MWNTs act as effective nucleating agents that significantly shorten the induction period of crystallization and however, decrease the crystallization rate of PCL, exhibiting a remarkable decrease in the Avrami exponent n, surface folding energy σe and crystallization activation energy ΔE. The carbon-based fillers act as templates for hard block chains of PCL to form an ordered structure on the surface of nanoparticles during the induction period, bringing about some increase in equilibrium temperature. The melting process of PCL and its nanocomposites are also studied; the nanocomposites exhibit two melting peaks at higher crystallization temperature which mainly refer to the melting of the crystals with different crystal sizes however, PCL shows only one melting temperature.

Keywords: poly(e-caprolactone)diol, multiwalled carbon nanotubes, composite materials, nonisothermal crystallization, crystal structure, nucleation

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Authors: Swati Tyagi, Syed Abbas

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Fractional-order Hopfield neural networks are generally used to model the information processing among the interacting neurons. To show the constancy of the processed information, it is required to analyze the stability of these systems. In this work, we perform Mittag-Leffler stability for the corresponding Caputo fractional-order bidirectional associative memory (BAM) neural networks with various time-delays. We derive sufficient conditions to ensure the existence and uniqueness of the equilibrium point by using the theory of topological degree theory. By applying the fractional Lyapunov method and Mittag-Leffler functions, we derive sufficient conditions for the global Mittag-Leffler stability, which further imply the global asymptotic stability of the network equilibrium. Finally, we present two suitable examples to show the effectiveness of the obtained results.

Keywords: bidirectional associative memory neural network, existence and uniqueness, fractional-order, Lyapunov function, Mittag-Leffler stability

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: S. Ghoudelbourk, A. Omeiri, D. Dib, H. Cheghib

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This paper shows that we can improve the performance of the auto-adjustable electric machines if a fractional dynamic is considered in the algorithm of the controlling order. This structure is particularly interested in the separate control of active and reactive power of the double-fed induction generator (DFIG) of wind power conversion chain. Fractional regulators are used in the regulation of chain of powers. Knowing that, usually, the source of DFIG is provided by converters through controlled rectifiers, all this system makes the currents of lines strongly polluted that can have a harmful effect for the connected loads and sensitive equipment nearby. The solution to overcome these problems is to replace the power of the rotor DFIG by multilevel inverters supplied by PV which improve the THD. The structure of the adopted adjustment is tested using Matlab/Simulink and the results are presented and analyzed for a variable wind.

Keywords: DFIG, fractional regulator, multilevel inverters, PV

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Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

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The FOPI controller is proposed based on the main properties of the decoupling control scheme, as well as the fractional calculus. By using the simplified decoupling technique, the transfer function of decoupled apparent process is firstly separated into a set of n equivalent independent processes in terms of a ratio of the diagonal elements of original open-loop transfer function to those of dynamic relative gain array and the fraction – order PI controller is then developed for each control loops due to the Bode’s ideal transfer function that gives the desired fractional closed-loop response in the frequency domain. The simulation studies were carried out to evaluate the proposed design approach in a fair compared with the other existing methods in accordance with the structured singular value (SSV) theory that used to measure the robust stability of control systems under multiplicative output uncertainty. The simulation results indicate that the proposed method consistently performs well with fast and well-balanced closed-loop time responses.

Keywords: ideal transfer function of bode, fractional calculus, fractional order proportional integral (FOPI) controller, decoupling control system

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Authors: F. Hamidi, N. Amiri, H. Mishmast Nehi

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The Bilevel Programming (BP) model has been presented for a decision making process that consists of two decision makers in a hierarchical structure. In fact, BP is a model for a static two person game (the leader player in the upper level and the follower player in the lower level) wherein each player tries to optimize his/her personal objective function under dependent constraints; this game is sequential and non-cooperative. The decision making variables are divided between the two players and one’s choice affects the other’s benefit and choices. In other words, BP consists of two nested optimization problems with two objective functions (upper and lower) where the constraint region of the upper level problem is implicitly determined by the lower level problem. In real cases, the coefficients of an optimization problem may not be precise, i.e. they may be interval. In this paper we develop an algorithm for solving interval bilevel linear fractional programming problems. That is to say, bilevel problems in which both objective functions are linear fractional, the coefficients are interval and the common constraint region is a polyhedron. From the original problem, the best and the worst bilevel linear fractional problems have been derived and then, using the extended Charnes and Cooper transformation, each fractional problem can be reduced to a linear problem. Then we can find the best and the worst optimal values of the leader objective function by two algorithms.

Keywords: best and worst optimal solutions, bilevel programming, fractional, interval coefficients

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Authors: Samaneh Rahimirshnani, Hossein Jafari

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In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process.

Keywords: queue length process, Malliavin calculus, covariance function, fractional Brownian motion, sub-fractional Brownian motion

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Authors: Dilip Depan, Austin Simoneaux, William Chirdon, Ahmed Khattab

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In this study, we present a novel approach to synthesize polymer nanocomposites with nanohybrid shish-kebab architecture (NHSK). For this low-density and high density polyethylene (PE) was crystallized on various carbon nano-fillers using a novel and convenient method to prepare high-yield NHSK. Polymer crystals grew epitaxially on carbon nano-fillers using a solution crystallization method. The mixture of polymer and carbon fillers in xylene was flocculated and precipitated in ethanol to improve the product yield. Carbon nanofillers of varying diameter were also used as a nucleating template for polymer crystallization. The morphology of the prepared nanocomposites was characterized scanning electron microscopy (SEM), while differential scanning calorimetry (DSC) was used to quantify the amount of crystalline polymer. Interestingly, whatever the diameter of the carbon nanofiller is, the lamellae of PE is always perpendicular to the long axis of nanofiller. Surface area analysis was performed using BET. Our results indicated that carbon nanofillers of varying diameter can be used to effectively nucleate the crystallization of polymer. The effect of molecular weight and concentration of the polymer was discussed on the basis of chain mobility and crystallization capability of the polymer matrix. Our work shows a facile, rapid, yet high-yield production method to form polymer nanocomposites to reveal application potential of NHSK architecture.

Keywords: carbon nanotubes, polyethylene, nanohybrid shish-kebab, crystallization, morphology

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Authors: Cisil Gulumser, Francesc Medina, Sevil Veli

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In this study, the synthesis of photocatalytic Bi₂WO₆ was practiced with simple heating processes and the effects of these treatments on the production of the desired compound were investigated. For this purpose, experiments with Bi(NO₃)₃.5H₂O and H₂WO₄ precursors were carried out to synthesize Bi₂WO₆ by four different combinations. These four combinations were grouped in two main sets as ‘treated in microwave reactor’ and ‘directly filtrated’; additionally these main sets were grouped into two subsets as ‘calcined’ and ‘not calcined’. Calcination processes were conducted at temperatures of 400ᵒC, 600ᵒC, and 800ᵒC. X-ray diffraction (XRD) and environmental scanning electron microscopy (ESEM) analyses were performed in order to investigate the crystal structure of powdered product synthesized with each combination. The highest crystallization of produced compounds was observed for calcination at 600ᵒC from each main group.

Keywords: bismuth tungstate, crystallization, microwave, photocatalysts

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Authors: Ramin Hosseinnezhad, Iurii Vozniak, Andrzej Galeski

Abstract:

Shear-induced crystallization, originated from orientation of chains along the flow direction, is an inevitable part of most polymer processing technologies. It plays a dominant role in determining the final product properties and is affected by many factors such as shear rate, cooling rate, total strain, etc. Investigation of the shear-induced crystallization process become of great importance for preparation of nanocomposite, which requires crystallization of nanofibrous sheared inclusions at higher temperatures. Thus, the effects of shear time, shear rate, and also thermal condition of cooling on crystallization of two aliphatic-aromatic copolyesters have been investigated. This was performed using Linkam optical shearing system (CSS450) for both Ecoflex® F Blend C1200 produced by BASF and synthesized copolyester of butylene terephthalate and a mixture of butylene esters: adipate, succinate, and glutarate, (PBASGT), containing 60% of aromatic comonomer. Crystallization kinetics of these biodegradable copolyesters was studied at two different conditions of shearing. First, sample with a thickness of 60µm was heated to 60˚C above its melting point and subsequently subjected to different shear rates (100–800 sec-1) while cooling with specific rates. Second, the same type of sample was cooled down when shearing at constant temperature was finished. The intensity of transmitted depolarized light, recorded by a camera attached to the optical microscope, was used as a measure to follow the crystallization. Temperature dependencies of conversion degree of samples during cooling were collected and used to determine the half-temperature (Th), at which 50% conversion degree was reached. Shearing ecoflex films for 45 seconds with a shear rate of 100 sec-1 resulted in significant increase of Th from 56˚C to 70˚C. Moreover, the temperature range for the transition of molten samples to crystallized state decreased from 42˚C to 20˚C. Comparatively low shift of 10˚C in Th towards higher temperature was observed for PBASGT films at shear rate of 600 sec-1 for 45 seconds. However, insufficient melt flow strength and non-laminar flow due to Taylor vortices was a hindrance to reach more elevated Th at very high shear rates (600–800 sec-1). The shift in Th was smaller for the samples sheared at a constant temperature and subsequently cooled down. This may be attributed to the longer time gap between cessation of shearing and the onset of crystallization. The longer this time gap, the more possibility for crystal nucleus to re-melt at temperatures above Tm and for polymer chains to recoil and relax. It is found that the crystallization temperature, crystallization induction time and spherulite growth of aliphatic-aromatic copolyesters are dramatically influenced by both the cooling rate and the shear imposed during the process.

Keywords: induced crystallization, shear rate, aliphatic-aromatic copolyester, ecoflex

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