Search results for: Fractional crystallization.

Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

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Authors: Rabha W. Ibrahim

Abstract:

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

Keywords: Fractional calculus, fractional differential equation, Lane-Emden equation, Riemann-Liouville fractional operators, Volterra integral equation.

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Authors: Xiang Li, Kui Chen, Bin Wu, Min Zhou

Abstract:

Sclareolide is made from sclareol by oxidiative synthesis and subsequent crystallization, while the crystallization mother liquor still contains 15%~30%wt of sclareolide to be reclaimed. With the reaction material of sclareol is provided as plant extract, many sorts of complex impurities exist in the mother liquor. Due to the difficulty in recycling sclareolide after solvent recovery, it is common practice for the factories to discard the mother liquor, which not only results in loss of sclareolide, but also contributes extra environmental burden. In this paper, a process based on adsorption and elution has been presented for recycling of sclareolide from mother liquor. After pretreatment of the crystallization mother liquor by HZ-845 resin to remove parts of impurities, sclareolide is adsorbed by HZ-816 resin. The HZ-816 resin loaded with sclareolide is then eluted by elution solvent. Finally, the eluent containing sclareolide is concentrated and fed into the crystallization step in the process. By adoption of the recycle from mother liquor, total yield of sclareolide increases from 86% to 90% with a stable purity of the final sclareolide products maintained.

Keywords: Sclareolide, resin, adsorption, chromatography.

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Authors: P. Worathanakul, P. Kongkachuichay

Abstract:

A new SUZ-4 zeolite membrane with tetraethlyammonium hydroxide as the template was fabricated on mullite tube via hydrothermal sol-gel synthesis in a rotating autoclave reactor. The suitable synthesis condition was SiO2:Al2O3 ratio of 21.2 for 4 days at 155 °C crystallization under autogenous pressure. The obtained SUZ-4 possessed a high BET surface area of 396.4 m2/g, total pore volume at 2.611 cm3/g, and narrow pore size distribution with 97 nm mean diameter and 760 nm long of needle crystal shape. The SUZ-4 layer obtained from seeding crystallization was thicker than that of without seeds or in situ crystallization.

Keywords: Membrane, seeding, sol-gel, SUZ-4 Zeolite.

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Authors: Jeeranun Neaungjumnong, Sasikarn Yairit, Sudarat Pattanapaiboonkul, Pramoch Rangsunvigit, Santi Kulprathipanja

Abstract:

Crystallization has been used for the separation of chloronitrobenzene or CNBs, which are isomeric substances (o-, mand p-CNB) and important intermediates in chemical productions. Effects of feed composition on the crystallization of m- and p-CNB was first studied. The results conform to the binary phase diagram of m- and p-CNB. After that, effects of FAU zeolites (NaX, CaX, BaX, NaY and CaY) above the eutectic composition (63.5 and 65.0 wt% m-CNB in the feed) was also investigated. The results showed that the FAU zeolites significantly affected the precipitates, the composition of which was shifted from being rich in m-CNB to rich in p-CNB. Effects of the number of FAU zeolites on the precipitate composition was then studied. The results revealed that the precipitates from the lower number of the zeolites had higher p-CNB purity than those from the higher number of zeolite.

Keywords: Chloronitrobenzenes, crystallization, separation, eutectic

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Authors: Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha

Abstract:

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

Keywords: Circuit design, fractional-order systems, genetic algorithms, logic circuits.

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

Abstract:

The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Keywords: Fractional calculus, fractional–order proportional integral controller, cascade control system, internal model control approach.

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Authors: Sanjaykumar R. Patel, Parth R. Kayastha

Abstract:

α-lactose monohydrate is widely used in the pharmaceutical industries as an inactive substance that acts as a vehicle or a medium for a drug or other active substance. It is a byproduct of dairy industries, and the recovery of lactose from whey not only boosts the improvement of the economics of whey utilization but also causes a reduction in pollution as lactose recovery can reduce the BOD of whey by more than 80%. In the present study, levels of process parameters were kept as initial lactose concentration (30-50% w/w), sonication amplitude (20-40%), sonication time (2-6 hours), and crystallization temperature (10-20 ^oC) for the recovery of lactose in ultrasound assisted cooling crystallization. In comparison with cooling crystallization, the use of ultrasound enhanced the lactose recovery by 39.17% (w/w). The parameters were optimized for the lactose recovery using Taguchi Method. The optimum conditions found were initial lactose concentration at level 3 (50% w/w), amplitude of sonication at level 2 (40%), the sonication time at level 3 (6 hours), and crystallization temperature at level 1 (10 °C). The maximum recovery was found to be 85.85% at the optimum conditions. Sonication time and the initial lactose concentration were found to be significant parameters for the lactose recovery.

Keywords: Crystallization, Taguchi method, ultrasound, lactose.

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Authors: Yung-Tan Lee, Ren-Yi Huang, Ju-Chin Chen, Jyh-Yi Shih, Meng-Lung Lin, Hsiao-Ling Yu, Yen-Tsui Hu, Chih-Cheng Chen

Abstract:

Cenozoic basalts found in Jiangsu province of eastern China include tholeiites and alkali basalts. The present paper analyzed the major, trace elements, rare earth elements of these Cenozoic basalts and combined with Sr-Nd isotopic compositions proposed by Chen et al. (1990)[1] in the literatures to discuss the petrogenesis of these basalts and the geochemical characteristics of the source mantle. Based on major, trace elements and fractional crystallization model established by Brooks and Nielsen (1982)[2] we suggest that the basaltic magma has experienced olivine + clinopyroxene fractionation during its evolution. The chemical compositions of basaltic rocks from Jiangsu province indicate that these basalts may belong to the same magmatic system. Spidergrams reveal that Cenozoic basalts from Jiangsu province have geochemical characteristics similar to those of ocean island basalts(OIB). The slight positive Nb and Ti anomalies found in basaltic rocks of this study suggest the presence of Ti-bearing minerals in the mantle source and these Ti-bearing minerals had contributed to basaltic magma during partial melting, indicating a metasomatic event might have occurred before the partial melting. Based on the Sr vs. Nd isotopic ratio plots, we suggest that Jiangsu basalts may be derived from partial melting of mantle source which may represent two-end members mixing of DMM and EM-I. Some Jiangsu basaltic magma may be derived from partial melting of EM-I heated by the upwelling asthenospheric mantle or asthenospheric diapirism.

Keywords: Geochemistry, Jiangsu Province, Cenozoic basalts, Fractional crystallization.

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Authors: Haniye Dehestani, Yadollah Ordokhani

Abstract:

In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: Collocation method, fractional partial differential equations, Legendre-Laguerre functions, pseudo-operational matrix of integration.

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Authors: Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha

Abstract:

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

Keywords: Circuit design, fractional-order systems, genetic algorithms, logic circuits

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Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman

Abstract:

This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.

Keywords: Analog Filter, Low-Pass Filter, Fractance, Sallen-Key, Stability.

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Authors: Bogdan Il. Bogdanov, Plamen S. Pashev, Yancho H. Hristov, Dimitar P.Georgiev, Irena G. Markovska

Abstract:

The crystallization kinetics and phase transformation of SiO2.Al2O3.0,56P2O5.1,8CaO.0,56CaF2 glass have been investigated using differential thermal analysis (DTA), x-ray diffraction (XRD), and scanning electron microscopy (SEM). Glass samples were obtained by melting the glass mixture at 14500С/120 min. in platinum crucibles. The mixture were prepared from chemically pure reagents: SiO2, Al(OH)3, H3PO4, CaCO3 and CaF2. The non-isothermal kinetics of crystallization was studied by applying the DTA measurements carried out at various heating rates. The activation energies of crystallization and viscous flow were measured as 348,4 kJ.mol–1 and 479,7 kJ.mol–1 respectively. Value of Avrami parameter n ≈ 3 correspond to a three dimensional of crystal growth mechanism. The major crystalline phase determined by XRD analysis was fluorapatite (Ca(PO4)3F) and as the minor phases – fluormargarite (CaAl2(Al2SiO2)10F2) and vitlokite (Ca9P6O24). The resulting glass-ceramic has a homogeneous microstructure, composed of prismatic crystals, evenly distributed in glass phase.

Keywords: glass-ceramic, crystallization, non-isothermalkinetics, Avrami parameter

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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Authors: Artion Kashuri, Rozana Liko

Abstract:

In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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Authors: Sachin Bhalekar

Abstract:

In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.

Keywords: Caputo derivative, delay, stability, chaos.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.

Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.

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Authors: Ki-Jin Kim, Sanghoon Park, K. H. Ahn

Abstract:

This paper presents the 20-GHz fractional PLL (Phase Locked Loop) circuit for the next generation Wi-Fi by using 90 nm TSMC process. The newly suggested millimeter wave 16/17 pre-scalar is designed and verified by measurement to make the fractional PLL having a low quantization noise. The operational bandwidth of the 60 GHz system is 15 % of the carrier frequency which requires large value of Kv (VCO control gain) resulting in degradation of phase noise. To solve this problem, this paper adopts AFC (Automatic Frequency Controller) controlled 4-bit millimeter wave VCO with small value of Kv. Also constant Kv is implemented using 4-bit varactor bank. The measured operational bandwidth is 18.2 ~ 23.2 GHz which is 25 % of the carrier frequency. The phase noise of -58 and -96.2 dBc/Hz at 100 KHz and 1 MHz offset is measured respectively. The total power consumption of the PLL is only 30 mW.

Keywords: Millimeter Wave Fractional PLL, Wide band VCO, WPAN Transceiver.

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Authors: Long Jye Sheu, Wei Ching Chen, Yen Chu Chen, Wei Tai Weng

Abstract:

In this paper, a two-channel secure communication using fractional chaotic systems is presented. Conditions for chaos synchronization have been investigated theoretically by using Laplace transform. To illustrate the effectiveness of the proposed scheme, a numerical example is presented. The keys, key space, key selection rules and sensitivity to keys are discussed in detail. Results show that the original plaintexts have been well masked in the ciphertexts yet recovered faithfully and efficiently by the present schemes.

Keywords: fractional chaotic systems, synchronization, securecommunication.

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Authors: P. Georgieva, S. Feyo de Azevedo

Abstract:

This paper is focused on issues of process modeling and two model based control strategies of a fed-batch sugar crystallization process applying the concept of artificial neural networks (ANNs). The control objective is to force the operation into following optimal supersaturation trajectory. It is achieved by manipulating the feed flow rate of sugar liquor/syrup, considered as the control input. The control task is rather challenging due to the strong nonlinearity of the process dynamics and variations in the crystallization kinetics. Two control alternatives are considered – model predictive control (MPC) and feedback linearizing control (FLC). Adequate ANN process models are first built as part of the controller structures. MPC algorithm outperforms the FLC approach with respect to satisfactory reference tracking and smooth control action. However, the MPC is computationally much more involved since it requires an online numerical optimization, while for the FLC an analytical control solution was determined.

Keywords: artificial neural networks, nonlinear model control, process identification, crystallization process

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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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Authors: Marcin Sowa

Abstract:

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

Abstract:

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: Mazidah Tajjudin, Mohd Hezri Fazalul Rahiman, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

In process control applications, above 90% of the controllers are of PID type. This paper proposed a robust PI controller with fractional-order integrator. The PI parameters were obtained using classical Ziegler-Nichols rules but enhanced with the application of error filter cascaded to the fractional-order PI. The controller was applied on steam temperature process that was described by FOPDT transfer function. The process can be classified as lag dominating process with very small relative dead-time. The proposed control scheme was compared with other PI controller tuned using Ziegler-Nichols and AMIGO rules. Other PI controller with fractional-order integrator known as F-MIGO was also considered. All the controllers were subjected to set point change and load disturbance tests. The performance was measured using Integral of Squared Error (ISE) and Integral of Control Signal (ICO). The proposed controller produced best performance for all the tests with the least ISE index.

Keywords: PID controller, fractional-order PID controller, PI control tuning, steam temperature control, Ziegler-Nichols tuning.

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Authors: S. Beyou, B. Grondin-Perez, M. Benne, C. Damour, J.-P. Chabriat

Abstract:

The industrial process of the sugar cane crystallization produces a residual that still contains a lot of soluble sucrose and the objective of the factory is to improve its extraction. Therefore, there are substantial losses justifying the search for the optimization of the process. Crystallization process studied on the industrial site is based on the “three massecuites process". The third step of this process constitutes the final stage of exhaustion of the sucrose dissolved in the mother liquor. During the process of the third step of crystallization (Ccrystallization), the phase that is studied and whose control is to be improved, is the growing phase (crystal growth phase). The study of this process on the industrial site is a problem in its own. A control scheme is proposed to improve the standard PID control law used in the factory. An auto-tuning PID controller based on instantaneous linearization of a neural network is then proposed.

Keywords: Auto-tuning, PID, Instantaneous linearization, Neural network, Non linear process, C-crystallisation.

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

Abstract:

This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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Authors: Petia Georgieva, Sebastião Feyo de Azevedo

Abstract:

This paper is focused on issues of nonlinear dynamic process modeling and model-based predictive control of a fed-batch sugar crystallization process applying the concept of artificial neural networks as computational tools. The control objective is to force the operation into following optimal supersaturation trajectory. It is achieved by manipulating the feed flow rate of sugar liquor/syrup, considered as the control input. A feed forward neural network (FFNN) model of the process is first built as part of the controller structure to predict the process response over a specified (prediction) horizon. The predictions are supplied to an optimization procedure to determine the values of the control action over a specified (control) horizon that minimizes a predefined performance index. The control task is rather challenging due to the strong nonlinearity of the process dynamics and variations in the crystallization kinetics. However, the simulation results demonstrated smooth behavior of the control actions and satisfactory reference tracking.

Keywords: Feed forward neural network, process modelling, model predictive control, crystallization process.

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Authors: U.K. Saha, L.K. Arora

Abstract:

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.

Keywords: Multiindex Mittag-Leffler function, Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration, Riemann-Liouville fractional integrals and derivatives.

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Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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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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