Fractional Kinetics Research Articles

Fractional neutron point kinetics model for reactivity transients of the NuScale and comparison with the classical kinetics approach

In this work, the behavior of the neutron and natural circulation parameters for Reactivity Transients in the PWR reactor called NuScale are analyzed through the novel system equations. It model includes non-integer and ordinary order differentials coupling the neutron point kinetic with the thermos-hydraulic core of the reactor. Transient processes of increase and decrease of the feed flow and the coolant inlet temperature are analyzed to identify the feedback of the thermohydraulic effects with the neutron phenomena in a non-integer order scheme. In the results, it is observed that for short times the power and reactivity have the same behavior with the classical model and the non-integer order model for all values of the anomalous diffusion coefficient simulated. However, for long times of simulation, there is more reactivity and less power, in contrast to the classical model, when reducing the value of the anomalous diffusion coefficient these counter-intuitive effects are increased. Additionally, a delay is observed between the change in reactivity and power. In conclusion, it is observed that sub-diffusive processes are relevant when there are slow changes in reactivity, which can be analyzed through the Fractional Order Neutron Density Equation.

Turbulence spreading by resonant wave-wave interactions: A fractional kinetics approach.

This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and witnessed a renewed attention in the literature recently. Here, we propose a comprehensive theory of turbulence spreading based on fractional kinetics. We argue that the use of fractional-derivative equationspermits a general approach focusing on fundamentals of the spreading process regardless of a specific turbulence model and/or specific instability type. The starting point is the Hamiltonian of resonant wave-wave interactions, from which a family of scaling laws for the asymptotic spreading is derived. Both three- and four-wave interactions are considered. The results span from a subdiffusive spreading in the parameter range of weak chaos to avalanche propagation in regimes with population inversion. Attention is paid to how nonergodicity introduces weak mixing, memory and intermittency into spreading dynamics, and how the properties of non-Markovianity and nonlocality emerge from the presence of islands of regular dynamics in phase space. Also we resolve an existing question concerning turbulence spillover into gap regions, where the instability growth is locally suppressed, and show that the spillover occurs through exponential (Anderson-like) localization in case of four-wave interactions and through an algebraic (weak) localization in case of triad interactions. In the latter case an inverse-cubic behavior of the spillover function is found. Wherever relevant, we contrast our findings against the available observational and numerical evidence, and we also commit ourselves to establish connections with the models of turbulence spreading proposed previously.

A Comparative Kinetic Study of Uncatalyzed and Ce(IV) Catalyzed Cetrizine Dihydrochloride Oxidation in Aqueous Acid Medium by Chloramine-T

A kinetic study of uncatalyzed and Ce(IV) catalyzed cetrizine dihydrochloride oxidation was carried out in aqueous acid medium using chloramine-T. Both uncatalyzed and catalyzed reactions follows first order kinetics with respect to [CAT] and fractional order kinetics with respect to [substrate]. The reaction follows first order dependence on [CeIV] catalyst. The uncatalyzed reaction shows inverse fractional order for [H+] and [Cl–] whereas catalyzed reaction follows fractional order. The effect of ionic strength is negligible in both cases. The dielectric constant has negative effect on uncatalyzed reaction and positive effect on catalyzed reaction. To compute the thermodynamic parameters the kinetic runs were studied at different temperatures (293-313 K). The stoichiometry of the reaction was studied and the products of oxidation were analyzed. The rate law was also derived by the proposed mechanism.

A new solution of the fractional neutron point kinetics equations using symmetry and the Heaviside's expansion formula

A new analytical solution of the Fractional Neutron Point Kinetics Equations is developed in the present work, considering multi-groups of precursors of delayed neutrons as well as a constant reactivity. Such solution is obtained in a short way, as a direct generalization of the integer case, being only necessary to use an elementary change of variable as well as the Heaviside's Expansion Formula. One of the most relevant novelties of the developed solution is that it has the same structure and mathematical form of the solution of the integer case. This symmetry property is an important advantage over other reported solutions because it allows extending, in a straightforward way, computational algorithms that are used for the integer case to the fractional one. A MATLAB code implementation of the developed solution is also provided, as well as numerical experiments, where the proposed analytical solution is applied to several cases and scenarios, observing a sub-diffusive behavior for step reactivities, a mixed profile for ramp simulations, as well as a displacement of the peaks in the case of feedback reactivities.

Electrospherization of genistein@DNA core-shell nanospheres as a drug delivery system and theoretical study of the release mechanism

Encapsulation of poor water-soluble drug was considered as one of the widely used approaches to overcome such obstacle. The goal of this research was in situ encapsulate the hydrophobic genistein (GEN) during the electrospherization (Es) of deoxyribonucleic acid (DNA) nanospheres as a delivery system with appropriate drug release properties. The prepared nanospheres (free GEN sample; Es DNA and GEN loaded DNA; Es GEN@DNA) were characterized using uv–visible spectroscopy (UV–vis), transmission electron microscope (TEM), zeta potential, Fourier transform infrared spectroscopy (FTIR), x-ray diffraction analysis (XRD), and stability test. In addition, the drug encapsulation % was studied, the drug release efficiency was recorded and theoretically visualized to understand the mechanism and kinetics of GEN drug release. The results revealed that GEN was successfully encapsulated during the DNA electrospherization as a core (GEN)/shell (DNA) like structure with a wonderful stability against time. The UV–vis patterns and their deconvolutions introduced that the emerged peak around 372–500 nm of Es GEN@DNA nanospheres has an area under curve larger than that of the free GEN sample. Zeta potential value decreased from −17.4 to −14.3 mV. In addition, TEM images confirmed the formation of a core/shell structure with average size 109.2 nm. XRD pattern of Es GEN@DNA revealed that GEN lost its crystalline phase, which indicated the incorporation of the drug. On the other hand, %Encapsulation of GEN within DNA nanospheres was found to be 89.62%. Es GEN@DNA release profile explored that the well entrapped GEN within the DNA nanospheres could be a promising for sustained drug release. Besides, the dilemma of using a fractal or fractional kinetics model was overcame by introducing a general fractional kinetic equation that involves a time-dependent rate coefficient, which introduced that the solution of the fractional kinetic model can fit the release data profiles.

Microstructure, deformation behavior, and dynamic recrystallization kinetics of FeNiMnCu-based high entropy alloys prepared by mechanical alloying and spark plasma sintering

In the present research, FeNiMnCuX (X: Co, Cr, Mo, Ti, W) high entropy alloys (HEAs) were successfully fabricated by mechanical alloying (MA) and spark plasma sintering (SPS). SPS transformed the base and Co-containing alloys into FCC structures, Cr- containing alloys changed into a mix of FCC and BCC structures, while other alloys formed a combination of FCC/BCC structure and an intermetallic compound. The base alloy and alloys with Co, and Cr additions exhibited plastic deformation in cold compression tests, whereas other alloys exhibited brittle behavior. During hot compression tests, dynamic recrystallization occurred with a peak in flow stress followed by a gradual decrease to a steady state stress in alloys with Co, Mo, Ti and W additions. The highest peak stresses were observed at 800 °C for Ti- and W- containing alloys. The dynamic recrystallization and fractional softening kinetics are explained by the Avrami kinetic model. An Avrami exponent around 1 was obtained based on the kinetics of dynamic recrystallization for the alloys doped with Co, Mo, Ti, and W.

Oxidation and TD-DFT of Toxic Acriflavine Hydrochloride Dye by Potassium Permanganate in Neutral Media: Kinetics and Removal of Dyes from Wastewater

Fabrication of dye thin films is accomplished through physical vapor deposition with a thickness of 150 ± 5 nm. Kinetically, the reduction of permanganate ion as a multi-equivalent oxidant by acriflavine hydrochloride (ACFH) in a neutral medium has been studied spectrophotometrically. In the presence of a pseudo-first-order reaction, the experimental results suggest fractional first-order kinetics in [ACFH] and a first-order dependency in [MnO4-]. The spectroscopic identification of intermediate species involving complexes of Mn (V) coordination has been examined along with a unique nitro-derivative-ACF (NDACF) synthesis. Based on the estimated activation values, which are in great agreement with the kinetic data obtained, oxidation reaction mechanism was postulated and described. The data exactly determine that ΔEgOpt the amount decreases from 1.566 eV for [ACFH]TF to 1.36 eV for [NDACF]TF for isolated molecules in the gaseous state utilizing TD-DFT model, HOMO and LUMO calculation. The improvements in kinetical and optical properties were achieved, and it is promising to use [NDACF]TF as solar cell application.

Numerical and computational analysis of fractional order mathematical models for chemical kinetics and carbon dioxide absorbed into phenyl glycidyl ether

The major objective of this effort is to use the collocation technique (CT) to examine fractional chemical kinetics(CK) and other problem that correlates the condensations of carbon dioxide (CO2) and phenyl glycidyl ether (PGE) with two varieties of Dirichlet and a mixed set of Neumann boundary and Dirichlet-type constraints respectively. The suggested approach depends on the shifted Jacobi collocation techniques along with the shifted Jacobi operational matrix for fractional derivatives of any order, defined in the Caputo sense. Examining a global approximation for temporal and spatial discretizations is the main benefit of the suggested methodology. Additionally, the mathematical method simplifies the fractional differential equations by reducing them to a straightforward problem that just needs the solution of a set of algebraic equations. The arithmetical results and figures show that the suggested approach is an effective algorithm with excellent accuracy for resolving arbitrary order differential equations. A few theorems regarding error analysis are presented and explained. We also compare the numerical results produced using the suggested technique with those results obtained through the existing techniques.

Kinetics and TD-DFT calculations of base-catalyzed oxidation of acriflavine hydrochloride: Removal of dyes colors from wastewater

The oxidation kinetics of acriflavine hydrochloride (AFH) to nitro-acriflavine (N-AFH) by KMnO4 as oxidizing agent in sodium hydroxide medium at a constant ionic strength of 0.5 moldm−3 was studied using spectrophotometric methods. It was found that the reaction went through two distinct steps that could be monitored. In the first stage, coordination species including transient blue pentavalent manganese and/or green hexavalent manganese species may be made quite quickly followed by the decomposition of intermediates in the second slow stage to produce soluble Mn (IV) and the nitroacriflavine as resulting products of oxidation. It has been investigated how several variables such as pH, ionic strength, permanganate ion concentration, and AFH substrate concentration affect oxidation rates. The experimental results demonstrated a first-order dependence in [MnO4−] and fractional first-order kinetics in each of [AFH] and alkali concentration under pseudo-first-order reaction conditions of [MnO4−] >>10 [AFH]. Sodium hydroxide concentrations accelerated the oxidation reaction, and as the alkali concentration rose, so the type of catalyzed is base-catalyzed. Evidence for the creation of a 1:1 intermediate complex was discovered using spectrophotometry and kinetics. In accordance with the kinetic findings, an efficient oxidation process that is compatible with the kinetic data obtained in terms of the activation parameters evaluated was analyzed, proposed, and debated. There are several techniques used to study the nanostructure thin films (AFH)TF and (N- AFH)TF, with using FT-IR, kinetic, isotherms of liquid-phase adsorption, and optical characteristics. A low deposition rate and a chamber pressure of 5 × 105 mbar are used in the PVD method to create (AFH)TF and (N-AFH)TF thin coatings with a 95 nanometer thickness. The isolated molecules (AFH)Iso and (N-AFH)Iso were additionally optimized using time-dependent density functional theory (TD-DFT) using TD-DFTD/Mol3 and Cambridge Serial Total Energy Bundle (TD-FDT/CASTEP). The optimized geometries, vibrational wavenumbers, intensity of vibrational bands, and various atomic charges of 9VC have all been investigated using DFT-B3LYP system using a 6-31G (d,p) basis set.

Photocatalytic water splitting kinetics of CMV model

The photocatalytic water splitting kinetics has been analyzed in this paper. The experimental data are taken from the published works and fitted with different theoretical models. From the results, we find that the photocatalytic kinetics of water splitting can be described by Capelas-Mainardi–Vaz (CMV) model very well. This suggests that the water splitting kinetics can be regarded as a fractional first-order kinetics of the chemical reaction. Also, we notice that photocatalytic water splitting is not always completely a monotone kinetics process.

Non-Local Kinetics: Revisiting and Updates Emphasizing Fractional Calculus Applications

Non-local kinetic problems spanning a wide area of problems where fractional calculus is applicable have been analyzed. Classical fractional kinetics based on the Continuum Time Random Walk diffusion model with the absence of stationary states, real-world problems from pharmacokinetics, and modern material processing have been reviewed. Fractional allometry has been considered a potential area of application. The main focus in the analysis has been paid to the memory functions in the convolution formulation, crossing from the classical power law to versions of the Mittag-Leffler function. The main idea is to revisit the non-local kinetic problems with an update updating on new issues relevant to new trends in fractional calculus.

Study on CO2 adsorption capacity and kinetic mechanism of CO2 adsorbent prepared from fly ash

The use of fly ash from coal-fired power plants for CO2 adsorption can reduce CO2 emissions and CO2 capture costs while making efficient use of power plant solid waste. In this study, fly ash was used to prepare aerogel support with good microstructure, and the support was impregnated with an incipient wetness impregnation method to make CO2 adsorbent. Adsorption experiments of CO2 adsorbents were carried out in a self-designed small fixed-bed reactor to study the influence of reaction conditions on the adsorption capacity of adsorbents. The results showed that the aerogel support prepared from fly ash had good microscopic properties with specific surface area and specific pore volume were 400 m2/g and 1.9 cm3/g, respectively. The pore structure was uniform, and the proportion of mesopores reached more than 99%. Under the reaction condition of 60 °C reaction temperature, 15% water vapor concentration, 15% CO2 concentration and 500 mL/min total gas flow rate, the maximum adsorption capacity of KA-30 adsorbent was 2.02 mmol/g. Avrami fractional kinetics model was used to calculate the cumulative adsorption capacity to study the adsorption kinetics. Combined with mass transfer kinetic model and deactivation model, the experimental breakthrough curve was fitted to study the adsorption mechanism of the adsorbent.

Drug Level Modelling with Difference and Differential Equations

In the current study, drug level in the human body is studied using mathematical modelling, where the difference equations have been used as a means of analyzing the dosage over a prescribed time, reduction in dose half-life, and the total amount of residual drug in the blood-stream for a given time-period. Further, the differential equations approach is investigated for data fitting using Mathematica to extend the application adhering to the continuous nature of the inherent function. The perspective helps to preserve critical resources and render comparative results. In this approach, zero-order, first-order, and fractional order kinetics are explored and compared.

Novel synthesis of antibacterial pyrone derivatives using kinetics and mechanism of oxidation of azithromycin by alkaline permanganate

Dimethylamino-2H-5-dihydropyrane-6-methyl-4-one (DADHP) is a novel antibacterial pyrones derivatives and potential pharmaceutical that was quantitatively synthesized by oxidizing azithromycin (AZ) antibiotic with potassium permanganate in an alkaline medium (pH > 12). The oxidation reaction was kinetically studied using spectrophotometric technique at ionic strength equal to 0.02 mol dm−3. The redox reaction was discovered to have two separate stages that could be measured. The first stage was relatively fast and corresponding to the formation of coordination intermediate complexes involving blue hypomanganate (V) and/or green manganate (VI) transient species. Variable parameters like as the concentration of permanganate ion and AZ substrate, as well as pH and ionic strength, have been studied to see how they affect oxidation rates. The experimental results showed a first-order dependency in [MnO4-] and fractional first-order kinetics in each of [AZ] and alkali concentration under pseudo-first-order reaction conditions of [AZ] ≫ 10 [MnO4-]. The oxidation process was base-catalyzed, and the oxidation rates increased as the alkali concentration increased. The product was confirmed by Fourier Transform Infrared spectroscopy (FTIR), elemental analysis, condensation tests with 2,4-dinitrophenyl haydrazine and hydroxyl amine, and GC-Mass. The oxidation product obtained can be employed as interesting class of organic compounds with diverse chemical and pharmacological applications.

Load-following control of a nuclear reactor using optimized FOPID controller based on the two-point fractional neutron kinetics model considering reactivity feedback effects

Load-following control of a nuclear reactor core is very crucial. The main challenge in examining power distribution control of the reactor core is to perform axial power distribution control rather than handling radial power distribution.In this work, a new model consisting of fractional order derivatives and two nodes of the reactor core with reactivity feedbacks is presented named as the two-point fractional neutron point kinetics (TPFNPK) model. According to neutron diffusion phenomena, this modeling method has a better physical interpretation for a quick change of neutron flux in load-following operation mode.For load-following control, a fractional order PID controller is implemented. Optimization of the parameters of this controller (KP, KI, λ, KD, and μ) is carried out utilizing a genetic algorithm (GA) which is an evolutionary algorithm.The objective is the minimization of the weighted sum of the integral of time-weighted absolute error (ITAE), and the overshoot or the undershoot (MP).The new reactor core model is simulated in a MATLAB/SIMULINK environment coupled with a genetic algorithm.Different load patterns (the assumed tracking signal) considering different values of the model parameter (α) are introduced to address the effectiveness of the implemented control method.The simulation result demonstrates that the optimized control methods (GA-PID and GA-FOPID) have satisfactory and suitable functionality during load pattern tracking for all selected values of the model parameter. However, the GA-FOPID controller has a relatively better performance compared to the GA-PID controller. In all cases, it has lower costs and faster convergence. In addition, core normalized axial offset (AO) is always maintained within a certain limit during load-following operation for all the cases. Furthermore, in all the cases, the normalized axial xenon oscillation index (AXOI) remains bounded during the power transient.

Kinetics of low radioactive wastewater imbibition and radionuclides sorption in partially saturated ternary-binder mortar

This study seeks to assess the imbibition kinetics of low radioactive wastewater (from the DayaBay nuclear power plant) into a partially saturated ternary-binder mortar, as well as the sorption kinetics of 60Co and 137Cs from the water. Mortar samples with the initial saturation degrees of 0, 0.4, 0.6, 0.8 and 1.0 were prepared for the wastewater treatment. Pore structure of the mortar was characterized using water vapor sorption isotherm and mercury intrusion porosimetry tests interpreted by the Guggenheim-Anderson-de Boer isothermal equilibrium, and volume- and energy-based fractal models. Results show that the mortar has consistent fractal pore structure between the models, and the liquid imbibitions follow the fractal imbibition kinetics, in which the parameters are non-linearly impacted by the initial saturation degrees. The sorption rate and retention capacity of 137Cs are much lower than those of 60Co, and both follow the Brouers–Sotolongo fractional kinetics. The findings uncover the complex liquid imbibition and radionuclides sorption kinetics in cement-based porous materials, and the in-situ data would contribute to the material designs and sorption controls for large scale in-situ treatments of wastewater from nuclear power plant.

Postprandial muscle protein synthesis rate is unaffected by 20-day habituation to a high protein intake: a randomized controlled, crossover trial.

During the last decade more researchers have argued in favor of an increased protein intake for older adults. However, there is a lack of knowledge on the long-term effects of conforming to such a high protein intake with regards to the basal and postprandial muscle protein turnover. The purpose of this study was to compare the postprandial synthesis response in muscle proteins, and the abundance of directly incorporated food-derived amino acids following habituation to high vs. recommended level of protein intake. In a double blinded crossover intervention 11 older male participants (66.6 ± 1.7years of age) were habituated for 20days to a recommended protein (RP) intake (1.1g protein/kg lean body mass (LBM)/day) and a high protein (HP) intake (> 2.1g protein/kg LBM/day). Following each habituation period, intrinsically labelled proteins were ingested as part of a mixed meal to determine the incorporation of meal protein-derived amino acids into myofibrillar proteins. Furthermore, the myofibrillar fractional synthesis rate (FSR) and amino acid kinetics across the leg were determined using gold standard stable isotope tracer methodologies. RT qPCR was used to assess the expression of markers related to muscle proteinsynthesis and breakdown. No impact of habituation was observed on skeletal muscle amino acid or protein kinetics. However, the shunting of amino acids directly from artery to vein was on average 2.9 [Formula: see text]mol/min higher following habituation to HP compared to RP. In older males, habituation to a higher than the currently recommended protein intake did not demonstrate any adaptions in the muscle protein turnover or markers hereof when subjected to an intake of an identical mixed meal. Journal number NCT02587156, Clinicaltrials.org. Date of registration: October 27th, 2015.

Base-catalyzed oxidation of poly (ethylene glycol) by alkaline permanganate: Part I. Kinetics and mechanism of formation of coordination intermediate complex

A spectrophotometric investigation has been applied to study the kinetics of oxidation of poly (ethylene glycol) (PEG) as a synthetic polymer by alkaline permanganate at a constant ionic strength of 1.0 mol.dm−3. The reaction was found to proceed through two distinct measurable stages. The first stage was relatively fast and corresponding to the formation of coordination polymer intermediate complexes involving blue hypomanganate (V) and/or green manganate (VI) transient species. The influence of variable factors on the oxidation rates such as the concentration of permanganate ion and PEG substrate concentrations as well as the pH and ionic strength have been examined. Under the pseudo-first-order reaction conditions of [PEG] ≫ [MnO4−], the experimental results showed a first-order dependence in [MnO4−] and fractional first-order kinetics in each of [PEG] and alkali concentration. The oxidation process was of base-catalyzed nature where the oxidation rates were increased with increasing the alkali concentration. The observed first-order rate constant was found to be 1.1 ×10−3 s−1 with deprotonation constant of 0.72 dm3 mol−1 at 45 °C. Blue hypomanganate (V) was detected for the first time by using a conventional spectrophotometer. The oxidation process has proceeded without the intervention of a free-radical mechanism. Colloidal manganese (IV) and the acid derivatives of PEG were identified as final oxidation products. The activation parameters of the second-order reaction have been calculated and found to be ΔH≠ = 40.66 kJmol−1; ΔS≠ = − 145.41 Jmol−K−1 and ΔG≠ = 83.99 kJmol−1. A plausible reaction mechanism for oxidation based on the evaluated activation parameters and in good consistent with the observed kinetic data was suggested and discussed.

Existence of a traveling wave solution in a free interface problem with fractional order kinetics

In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0<α<1. We turn the free interface problem into a scalar free boundary problem coupled with an integral equation. The main intermediary step is to reduce the scalar problem to the study of a non-Lipschitz vector field in dimension 2. The latter is treated by qualitative topological methods based on the Poincaré-Bendixson Theorem. The phase portrait is determined and the existence of a stable manifold at the origin is proved. A significant result is that the settling time to reach the origin is finite, meaning that the trailing interface is finite in contrast to the case α=1, but in accordance with α=0. Finally, the integro-differential system is solved via a fixed-point method.

Synergistic activity of weak organic acids against uropathogens

Urinary tract infections (UTIs) are among the most common hospital-acquired infections, with an estimated 75% of UTIs caused by urinary catheters. In addition to the significant healthcare costs and patient morbidity, the escalating antimicrobial resistance reported among common uropathogens make the investigation of efficacious new antimicrobial strategies of urgent importance. To examine the antibacterial activity of a suite of weak organic acids (WOAs) (citric acid, malic acid, propionic acid, mandelic acid, lactic acid, benzoic acid, pyruvic acid and hippuric acid), alone and in combination, against common nosocomial uropathogens (Proteus mirabilis, Staphylococcus aureus, Escherichia coli and Pseudomonas aeruginosa). Minimum inhibitory concentration (MIC), minimum bactericidal concentration (MBC), minimum biofilm eradication concentration (MBEC), fractional inhibitory concentration index (FICI) values and kinetics of bactericidal activity of WOAs were determined by microdilution and time-kill assays. All tested WOAs displayed bactericidal activities against uropathogens in their planktonic and biofilm modes of growth when used individually. Moreover, WOAs in combination displayed synergistic activity against P.mirabilis, S. aureus and E.coli, with reductions in MIC values of up to 250-fold and significant reductions in biofilm formation. The synergistic multi-mechanistic combinations identified herein are anticipated to play an important role in the treatment and prevention of catheter-associated UTIs.