Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative

We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the “fractional centered derivative” approach. We determine the error of the Riesz fractional derivative to the fractional centered difference. We apply the Crank–Nicolson method to a fractional diffusion equation which has the Riesz fractional derivative, and obtain that the method is unconditionally stable and convergent. Numerical results are given to demonstrate the accuracy of the Crank–Nicolson method for the fractional diffusion equation with using fractional centered difference approach.     

Solving a large-scale crew pairing problem

Airline companies seek to solve the problem of determining an assignment of crews to a pre-determined flight schedule with minimum total cost, called the Crew Pairing Problem (CPP). Most of the existing studies focus on the CPP of North American airlines, which widely differs from that of most European airline companies in terms of the objective function, the flight structure, and the planning horizon. In this study, we develop an optimization-driven heuristic algorithm that can efficiently handle large-scale instances of the CPP that must be solved on a monthly basis. We perform computational experiments using flight schedules of an European airline company to test the performance of the solution method. Our computational results demonstrate that our algorithm is able to provide high-quality solutions to monthly instances with up to 27?000 flight legs.     

Determination of Minimum Enzymatic Decolorization Time of Reactive Dye Solution by Spectroscopic & Mathematical Approach

Synthetic dyes are very important for textile dyeing,paper printing,color photography and petroleum products.Traditional methods of dye removal include biodegradation,precipitation,adsorption,chemical degradation,photo degradation,and chemical coagulation.Dye decolorization with enzymatic reaction is an important issue for several research field(chemistry,environment)In this study,minimum decolorization time of Remazol Brilliant Blue R dye with Horseradish peroxidase enzyme was calculated using with mathematical equation depending on experimental data.Dye decolorization was determined by monitoring the absorbance decrease at the specific maximum wavelength for dye.All experiments were carried out with different initial dye concentrations of Remazol Brilliant Blue R at 25 ℃ constant temperature for 30 minutes.The development of the least squares estimators for a nonlinear model brings about complications not encountered in the case of the linear model.Decolorization times for completely removal of dye were calculated according to equation.It was shown that mathematical equation was conformed exponential curve for dye degradation.     

Enzymatic Decolorization of Anthraquinone and Diazo Dyes Using Horseradish Peroxidase Enzyme Immobilized onto Various Polysulfone Supports

In this study, covalent immobilization of the horseradish peroxidase (HRP) onto various polysulfone supports was investigated. For this purpose, different polysulfones were methacrylated with methacryloyl chloride, and then, nonwoven fabric samples were coated by using solutions of these methacrylated polysulfones. Finally, support materials were immersed into aquatic solution of HRP enzyme for covalent immobilization. Structural analysis of enzyme immobilization onto various polysulfones was confirmed with Fourier transform infrared spectroscopy, atomic force microscopy, and proton nuclear magnetic resonance spectroscopy. Decolorization of textile diazo (Acid Black 1) and anthraquinone (Reactive Blue 19) dyes was investigated by UV–visible spectrophotometer. Covalently immobilized enzyme has been used seven times in freshly prepared dye solutions through 63 days. Dye decolorization performance of the immobilized systems was observed that still remained high (70 %) after reusing three times. Enzyme activities of immobilized systems were determined and compared to free enzyme activity at different conditions (pH, temperature, thermal stability, storage stability). Enzyme activities of immobilized systems and free enzyme were also investigated at the different temperatures and effects of temperature and thermal resistance for different incubation time at 50 °C. In addition, storage activity of free and immobilized enzymes was determined at 4 °C at different incubation days.     

Urease-Dextran complexes with enhanced enzymatic activity and stability

In this study, the urease-dextran non-covalent complexes in various molar ratios were synthesized and compared to the free enzyme in terms of pH, temperature, thermal and storage stabilities. Especially, the complex with a molar ratio of n_U/n_DA = 40/1 showed highest thermal stability and had ca. 1.4-fold at 25°C and 2.5-fold at 80°C higher activity than the free enzyme. The complex showed a high catalytic activity in organic solvent. In addition, the thermal and storage stabilities of urease were improved greatly as dextran complex, which has advantages for usage in practice.     

Effects of cosolvents cetyltrimethylammonium bromide on the thresholds for nucleation of nitrogen in aqueous solutions

The decomposition of ammonium nitrite in water creates a supersaturated solution of nitrogen. The same process occurs in water-organic solvent mixtures. Acetone, dioxane, dimethylsulfoxide (DMSO) and dimethylformamide (DMF) are the cosolvents used in this study. The limits of supersaturation of nitrogen (C _SL /mol L^–1) were determined in all of these solvent mixtures by releasing the dissolved gas sonicationally and measuring the volume of released gas. C _SL was generally increased in the presence of cosolvents. The effectiveness sequence of organic solvents was found to be as DMF SL and all of the measured quantities of this study were generally affected by micelle formation.     

Spectral studies of safranin-O in different surfactant solutions

The interaction of Safranin-O (SO), a cationic dye, with various surfactants viz., anionics; Sodiumdodecylsulfate (SDS) and Sodiumdodecylsulfonate (SDSo), nonionics; polyoxyethylenesorbitanmonolaurate (Tween 20) and polyoxyethylenedodecylether (Brij 35), cationic; Dodecyltrimethylammoniumbromide (DTAB) and zwitterionic; Laurylsulfobetaine (LSB) was studied spectrophotometrically as a function of surfactant concentration ranging from premicellar to postmicellar region in aqueous media in the absence and presence of cosolvents. The binding constants (K(b)) and fraction of bound SO to micelles (f), were calculated by means of Benesi-Hildebrand Equation. The binding tendency of SO to micelles followed the order as; Tween 20>Brij 35>SDS>SDSo>LSB. The presence of cosolvents, such as Methanol, Dimethylformamide (DMFA) and 1,4 Dioxan (DX) at various volume percentages, increased the CMC of both SDS and Tween 20 and at a certain concentration totally inhibited the micellization. The binding of SO to micelles decreased as the concentration of the cosolvents increased. This inhibitory effect of cosolvents on binding of SO to micelles followed the order as; Methanol>DMFA>DX.     

An Updated Portrait of Transition to Turbulence in Laminar Pipe Flows with Periodic Time Dependence (A Correlation Study)

Transition to turbulence in axially symmetrical laminar pipe flows with periodic time dependence classified as pure oscillating and pulsatile (pulsating) ones is the concern of the paper. The current state of art on the transitional characteristics of pulsatile and oscillating pipe flows is introduced with a particular attention to the utilized terminology and methodology. Transition from laminar to turbulent regime is usually described by the presence of the disturbed flow with small amplitude perturbations followed by the growth of turbulent bursts. The visual treatment of velocity waveforms is therefore a preferred inspection method. The observation of turbulent bursts first in the decelerating phase and covering the whole cycle of oscillation are used to define the critical states of the start and end of transition, respectively. A correlation study referring to the available experimental data of the literature particularly at the start of transition are presented in terms of the governing periodic flow parameters. In this respect critical oscillating and time averaged Reynolds numbers at the start of transition; Re _os,crit and Re _ta,crit are expressed as a major function of Womersley number, $\sqrt {\omega ^\prime } $ defined as dimensionless frequency of oscillation, f. The correlation study indicates that in oscillating flows, an increase in Re _os,crit with increasing magnitudes of $\sqrt {\omega ^\prime } $ is observed in the covered range of $1<\sqrt {\omega ^\prime } <72$ . The proposed equation (Eq. 7), ${\rm{Re}}_{os,crit} ={\rm{Re}}_{os,crit} \left( {\sqrt {\omega ^\prime } } \right)$ , can be utilized to estimate the critical magnitude of $\sqrt {\omega ^\prime }$ at the start of transition with an accuracy of ±12?% in the range of $\sqrt {\omega ^\prime } <41$ . However in pulsatile flows, the influence of $\sqrt {\omega ^\prime }$ on Re _ta,crit seems to be different in the ranges of $\sqrt {\omega ^\prime } <8$ and $\sqrt {\omega ^\prime } >8$ . Furthermore there is rather insufficient experimental data in pulsatile flows considering interactive influences of $\sqrt {\omega ^\prime } $ and velocity amplitude ratio, A ₁. For the purpose, the measurements conducted at the start of transition of a laminar sinusoidal pulsatile pipe flow test case covering the range of 0.21<?A ₁?<0.95 with $\sqrt {\omega ^\prime } <8$ are evaluated. In conformity with the literature, the start of transition corresponds to the observation of first turbulent bursts in the decelerating phase of oscillation. The measured data indicate that increase in $\sqrt {\omega ^\prime } $ is associated with an increase in Re _ta,crit up to $\sqrt {\omega ^\prime } =3.85$ while a decrease in Re _ta,crit is observed with an increase in $\sqrt {\omega ^\prime } $ for $\sqrt {{\omega }'} >3.85$ . Eventually updated portrait is pointing out the need for further measurements on i) the end of transition both in oscillating and pulsatile flows with the ranges of $\sqrt {\omega ^\prime } <8$ and $\sqrt {\omega ^\prime } >8$ , and ii) the interactive influences of $\sqrt {\omega ^\prime } $ and A ₁ on Re _ta,crit in pulsatile flows with the range of $\sqrt {\omega ^\prime } >8$ .