Fractional Method Research Articles

Research on Evaluation Method of Water-blocking Powder Distribution Uniformity of Buffer Layer in HV Cable Based on Image Processing

Abstract High voltage (HV) cables are widely used in urban power transmission networks. The key component in HV cable, the buffer layer, has attracted lots of attention and more and more researchers are devoting to its material property evaluation and quality test techniques. A longitude water-blocking property evaluation method of buffer layer based on image processing is proposed in this paper. The microscopic images of the buffer layer are enhanced and morphologically processed. The area fraction method, entropy method, and fractal dimension method are used to evaluate the distribution characteristics of buffer layer water-blocking powder in binary images. This article innovatively proposes a more economical and convenient simulation method that can efficiently and accurately evaluate the waterproof performance of the buffer layer of high-voltage cables. With the proper use of the buffer layer, it can effectively protect the cables and improve the stability of power system operation.

Efficient modeling of fractional Laplacian viscoacoustic wave equation with fractional finite-difference method

The fractional viscoacoustic/viscoelastic wave equation, which accurately quantifies the frequency-independent anelastic effects, has been the focus of seismic industry in recent years. The pseudo-spectral (PS) method stands as one of the most widely used numerical methods for solving the fractional wave equation. However, the PS method often suffers from low accuracy and efficiency, particularly when modeling wave propagation in heterogeneous media. To address these issues, we propose a novel and efficient fractional finite-difference (FD) method for solving the wave equation with fractional Laplacian operators. This method develops an arbitrary high-order FD operator via the generating function of our fractional FD (F-FD) scheme, enhancing accuracy with L2-optimal FD coefficients. Similar to classic FD methods, our F-FD method is characterized by straightforward programming and excellent 3D extensibility. It surpasses the PS method by eliminating the need for Fast Fourier Transform (FFT) and inverse-FFT (IFFT) operations at each time step, offering significant benefits for 3D applications. Consequently, the F-FD method proves more adept for wave-equation-based seismic data processes like imaging and inversion. Compared with existing F-FD methods, our approach uniquely approximates the entire fractional Laplacian operator and stands as a local numerical algorithm, with an adjustable F-FD operator order based on model parameters for enhanced practicality. Accuracy analyses confirm that our method matches the precision of the PS method with a correctly ordered F-FD operator. Numerical examples show that the proposed method has good applicability for complex models. Finally, we have carried out reverse time migration on the Marmousi-2 model, and the imaging profiles indicate that the proposed method can be effectively applied to seismic imaging, demonstrating good practicability.

Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent

Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent

Fourier–Gegenbauer Pseudospectral Method for Solving Periodic Higher-Order Fractional Optimal Control Problems

Optimal control (OC) problems involve determining the best control strategy for a system to achieve the desired outcome. Fractional-order OC models have emerged in recent decades to represent complex systems that exhibit memory effects and nonlocal interactions. These models offer advantages over the traditional integer-order models. However, a key challenge with existing fractional calculus methods to define fractional derivatives, such as Riemann–Liouville, Caputo, and Grünwald–Letnikov derivatives, is that they often fail to maintain the periodic nature of dynamical systems. This limitation hinders their application to real-world scenarios, in which periodicity is crucial. This study proposes a novel model for periodic higher-order fractional OC problems (PHFOCPs). We achieve this by employing recently developed periodic fractional derivatives that specifically preserve the periodicity within the model. This study outlines also a robust numerical solution method for this new class of problems. The numerical method is applicable for any positive fractional order [Formula: see text] and leverages several key techniques, including a useful change of variables, Fourier collocation, and Fourier and Gegenbauer quadratures, to retain numerical stability and high accuracy. We theoretically prove the exponential convergence of the proposed numerical method for sufficiently smooth periodic functions. The effectiveness of the proposed approach is further validated through various numerical simulations. In essence, this work presents a novel framework for the OC of periodic systems using fractional calculus, overcoming the limitations of classical methods and offering a powerful tool for various scientific and engineering applications.

Mild extraction of faba bean (Vicia faba L.) proteins against conventional methods: Impact on physicochemical and thermal characteristics

Faba bean (high- and low-tannin) protein isolates were water extracted followed by dialysis or micellization in comparison to concentrates from conventional alkali extraction + acid precipitation, and salt-based extraction (1% NaCl) + dialysis. Protein fractions were characterised for secondary structure conformational changes, crystalline structure, particle size distribution in aqueous suspension and thermal properties. Mild water or salt extraction did not influence particle size distribution. Based on XRD, FTIR and CD, β-sheet structures were the most abundant secondary structures and water extraction + dialysis had minimal impact on their native conformation. DSC results showed an association between protein purity, glass transition temperature and endothermic enthalpy. High melting temperature above glass transition confirms the suitability of faba bean proteins for thermal/extrusion processing. Fractionation method was a more significant determinant of physicochemical characteristics compared to the cultivar. Further exploration of the techno-functional characteristics of faba bean proteins is essential for value-added food applications.

A fast and sensitive size-exclusion chromatography method for plasma extracellular vesicle proteomic analysis.

Extracellular vesicles (EVs) carry diverse biomolecules derived from their parental cells, making their components excellent biomarker candidates. However, purifying EVs is a major hurdle in biomarker discovery since current methods require large amounts of samples, are time-consuming and typically have poor reproducibility. Here we describe a simple, fast, and sensitive EV fractionation method using size exclusion chromatography (SEC) on a fast protein liquid chromatography (FPLC) system. Our method uses a Superose 6 Increase 5/150, which has a bed volume of 2.9mL. The FPLC system and small column size enable reproducible separation of only 50µL of human plasma in 15min.To demonstrate the utility of our method, we used longitudinal samples from a group of individuals who underwent intense exercise. A total of 838 proteins were identified, of which, 261 were previously characterized as EV proteins, including classical markers, such as cluster of differentiation (CD)9 and CD81. Quantitative analysis showed low technical variability with correlation coefficients greater than 0.9 between replicates. The analysis captured differences in relevant EV proteins involved in response to physical activity.Our method enables fast and sensitive fractionation of plasma EVs with low variability, which will facilitate biomarker studies in large clinical cohorts.

New computational approaches to the fractional coupled nonlinear Helmholtz equation

PurposeThe main aim of this paper is to investigate the fractional coupled nonlinear Helmholtz equation by two new analytical methods.Design/methodology/approachThis article takes an inaugural look at the fractional coupled nonlinear Helmholtz equation by using the conformable derivative. It successfully finds new fractional periodic solutions and solitary wave solutions by employing methods such as the fractional method and the fractional simple equation method. The dynamics of these fractional periodic solutions and solitary wave solutions are then graphically represented in 3D with appropriate parameters and fractal dimensions. This research contributes to a deeper comprehension and detailed exploration of the dynamics involved in high dimensional solitary wave propagation.FindingsThe proposed two mathematical approaches are simple and efficient to solve fractional evolution equations.Originality/valueThe fractional coupled nonlinear Helmholtz equation is described by using the conformable derivative for the first time. The obtained fractional periodic solutions and solitary wave solutions are completely new.

Label-free single-vesicle based surface enhanced Raman spectroscopy: A robust approach for investigating the biomolecular composition of small extracellular vesicles.

Small extracellular vesicles (sEVs) are cell-released vesicles ranging from 30-150nm in size. They have garnered increasing attention because of their potential for both the diagnosis and treatment of disease. The diversity of sEVs derives from their biological composition and cargo content. Currently, the isolation of sEV subpopulations is primarily based on bio-physical and affinity-based approaches. Since a standardized definition for sEV subpopulations is yet to be fully established, it is important to further investigate the correlation between the biomolecular composition of sEVs and their physical properties. In this study, we employed a platform combining single-vesicle surface-enhanced Raman spectroscopy (SERS) and machine learning to examine individual sEVs isolated by size-exclusion chromatography (SEC). The biomolecular composition of each vesicle examined was reflected by its corresponding SERS spectral features (biomolecular "fingerprints"), with their roots in the composition of their collective Raman-active bonds. Origins of the SERS spectral features were validated through a comparative analysis between SERS and mass spectrometry (MS). SERS fingerprinting of individual vesicles was effective in overcoming the challenges posed by EV population averaging, allowing for the possibility of analyzing the variations in biomolecular composition between the vesicles of similar and/or different sizes. Using this approach, we uncovered that each of the size-based fractions of sEVs contained particles with predominantly similar SERS spectral features. Indeed, more than 84% of the vesicles residing within a particular group were clearly distinguishable from that of the other EV sub-populations, despite some spectral variations within each sub-population. Our results suggest the possibility that size-based EV fractionation methods produce samples where similarly eluted sEVs are correlated with their respective biochemical contents, as reflected by their SERS spectra. Our findings therefore highlight the possibility that the biogenesis and respective biological functionalities of the various sEV fractions may be inherently different.

Scale-up of a sorption process working with molecularly imprinted adsorbents for enrichment of winemaking residues and improvement of bioactivity

This work presents the scale-up of a sorption process for the fractionation and enrichment of bioactive compounds in winemaking residues using molecularly imprinted adsorbents. The process works with hydroalcoholic solvents and the improvement of the bioactivity of the produced fractions, comparatively to the raw extracts, is demonstrated. The proposed approach was experimentally validated through the designing and running of a pilot size sorption prototype for the automation of the fractionation method. The synthesis of the molecularly imprinted adsorbents was made at the gram-scale and spent diatomaceous earth, used for wine filtration, was considered as a possible source of bioactive compounds in winemaking residues.The different fractions produced were evaluated for their antioxidant activity through three different assays, namely radical scavenging activity, reducing power and inhibition of lipid peroxidation. The results obtained show the improvement of the bioactivity of most of the fractions comparatively to the original diatomaceous earth extract. The most enriched fraction is estimated to have a total phenolic content c.a. 3.8 times higher than the original extract. The radical scavenging activity, the reducing power and the inhibition of lipid peroxidation for this fraction were measured to be 6.4, 4.2 and 4.5 times higher, respectively, than the initial diatomaceous earth extract.This work provides new insights on biomass valorisation and circular bioeconomy by combining in the same research materials development, process design and application to real extracts with proved improvement of the bioactivity of purified products.

Fractional Boundary Element Solution for Nonlinear Nonlocal Thermoelastic Problems of Anisotropic Fibrous Polymer Nanomaterials

This paper provides a new fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems with anisotropic fibrous polymer nanoparticles. This comprehensive BEM solution comprises two solutions: the anisotropic fibrous polymer nanoparticles problem solution and the nonlinear nonlocal thermoelasticity problem. The nonlinear nonlocal thermoelasticity problem solution separates the displacement field into complimentary and specific components. The overall displacement is obtained using the boundary element methodology, which solves a Navier-type problem, and the specific displacement is derived using the local radial point interpolation method (LRPIM). The new modified shift-splitting (NMSS) technique, which minimizes memory and processing time requirements, was utilized to solve BEM-created linear systems. The performance of NMSS was evaluated. The numerical results show how fractional and graded parameters influence the thermal stresses of nonlinear nonlocal thermoelastic issues involving anisotropic fibrous polymer nanoparticles. The numerical findings further reveal that the BEM results correlate very well with the finite element method (FEM) and analytical results, demonstrating the validity and correctness of the proposed methodology.

Determination method for binary fractions using the integrated spectrum

ABSTRACT We need to resolve the individual stars for binary-fraction determinations of stellar systems. Therefore, it is not possible to obtain the binary fractions for dense or distant stellar systems. We propose a method to determine the binary fraction of a dense or distant stellar system: this method is first to determine the binary-fraction variation for any two adjacent regions and then to add up those binary-fraction variations along the radial direction to obtain the binary fraction for a stellar system. The binary-fraction variation is derived using 10 binary-fraction-sensitive spectral absorption feature indices (SAFIs) and the binary-fraction variation calibrations in terms of these SAFIs. Using this method, we first present the binary-fraction variations for 21 Galactic globular clusters (GCs). By comparison, we find that they agree well with the binary fractions based on the main-sequence fiducial line method from previous studies. This verifies that the above-mentioned method is feasible. Next, we present the binary-fraction variations of 13 Galactic GCs. We give the relationships between the binary fraction and various parameters, and find that the binary fraction is negatively correlated with NHB and NRR, the binary fraction of some studies is not strongly correlated with NBS, and the number of GCs with large binary fraction is greater for the extreme blue horizontal branch population ratio. Finally, if we want to obtain a more accurate binary fraction, we suggest that spectroscopic and photometric observations are conducted at an appropriate area interval for a stellar system.

Effects of short-time work schemes on firm survival during the covid-19 crisis: insights from new Spanish data

ABSTRACT This paper explores the effect of Short-time Work Schemes (STW) on firm survival, analysing aggregated survival rates in a large cohort of more than a million employers followed during the onset of the COVID-19 pandemic in Spain. These public schemes were widely used during the pandemic and temporarily subsidized employees' wages, relieving labour downsizing costs to the employers. We apply fractional regression methods to this novel database that links STW take-up with firm survival rates from administrative sources. Our results suggest a positive association between firm survival and the STW take-up of their employees. We argue this effect, although not causal, informs of a lower bound with selection bias likely operating in the opposite direction, since a priori vulnerable firms are more likely to adopt the scheme. We also argue that this more intensive use may drive the heterogeneous results which pointed at stronger effects on vulnerable sectors and smaller firms.

Design and Validation of a High-Throughput Reductive Catalytic Fractionation Method

Design and Validation of a High-Throughput Reductive Catalytic Fractionation Method

Iterated fractional Tikhonov method for recovering the source term and initial data simultaneously in a two-dimensional diffusion equation

In this paper, an inverse problem of a two-dimensional diffusion equation is considered. The purpose here includes recovering not only the source term but also the initial value from given observations at two fixed times t=T1 and t=T2. The uniqueness of the solutions for the inverse problem is given. Instead of the classical Tikhonov regularization strategy, we propose an iterated fractional Tikhonov regularization method to solve this problem, an a priori and an a posterior parameter selection rules and corresponding convergence rates are derived. For verification of the theoretical estimates, several numerical examples are constructed and compared with the standard iterated Tikhonov regularization method.

Eulerian–Lagrangian multiscale numerical analysis of multimodal partial shedding dynamics

The objective of this paper is to investigate the multimodal partial shedding dynamics from a multiscale perspective of cloud cavitating flows under two distinct cavity shedding mechanisms, namely the re-entrant jet mechanism and the shock wave propagation mechanism. A two-way Eulerian–Lagrangian coupling algorithm is applied to capture the multiscale vapor topologies from microbubble to large-scale cavities. The large-scale cavity evolution is solved through large eddy simulations (LES) with the volume of fraction (VOF) method in Eulerian frame. The sub-grid microbubbles are tracked in Lagrangian frame based on the discrete bubble model (DBM) method. The predictions agree well with experimental observation of the periodical cavity evolution and microbubble dynamics under both the re-entrant jet mechanism and shock wave mechanism around a NACA66 hydrofoil. The numerical simulation provides detailed analysis of the cavitating turbulent flow on the microbubble behavior with emphasis on the spatial-temporal distribution characteristics of microbubbles. The results show that the number and mean size of microbubbles in the cavitation region increase gradually with the growth of attached sheet cavity, development of re-entrant jet and collapse of largescale cavity for both cavitation patterns. Meanwhile, microbubbles are mainly distributed on the largescale interfaces where have high value of vorticity and turbulent kinetic energy under the effect of re-entrant jet and vortex structures. And the probability density functions (PDFs) of microbubble exhibit gamma distributions with a dominant peak at approximately 50 μm for both shedding mechanisms. However, the shock wave formation and propagation process only occurs in the final stage of cavitating flow under shock wave mechanism causing the condensation of vapor and the decrease of the number and mean size of microbubbles. Moreover, the microbubbles are uniformly distributed along the streamwise and vertical directions behind shock wave front.

Effect of Dry and Wet Fractionation on Nutritional and Physicochemical Properties of Faba Bean and Yellow Pea Protein

ABSTRACTPlant‐based proteins continue to gain popularity as a sustainable alternative to animal proteins due to their nutritional, functional and health benefits. Dry and wet fractionation methods are increasingly being used for the production of value‐added pulse protein ingredients. The objective of this study was to compare the nutritional properties, protein quality, physicochemical properties and secondary structure of Australian faba bean and yellow pea protein concentrates and protein isolates obtained by dry and wet fractionation. Amino acid scores highlighted that faba bean and yellow pea protein isolates and concentrates were deficient in the sulphur‐containing amino acids, methionine and cysteine and tryptophan. Faba bean (63.7%) and yellow pea protein (63.0%) isolates had higher in vitro protein digestibility‐corrected amino acid scores compared to the protein concentrates, being 50.7% and 54.4%, respectively. Fourier‐transform infrared spectroscopy revealed different secondary structures between protein concentrates and isolates, especially for the amide I region. Faba bean and yellow pea protein concentrates had higher protein solubility (46.2% and 50.1%, respectively) and higher foaming capacity (65% and 59%, respectively) compared to the protein isolates. Water‐holding capacity was higher for faba bean and yellow pea protein isolates, being 4.3% and 4.0 g/g, respectively. These findings demonstrate that faba bean and yellow pea protein concentrates and isolates have unique functional properties that can be exploited for use in a diverse range of new and existing food applications.

Exploring Advanced Analysis Technique for Shallow Water Flow Models with Diverse Applications

The present article focuses on the analytical approach using fractional orders and its applicationin the dynamics of physical processes. Fractional order models align better with experimental data compared tonon-fractional ones. This study primarily focuses on employing the new approximate analytical method to solveshallow water models with fractional orders. Numerical examples within the Caputo fractional derivative showcasethe method’s application. Results for both integer and fractional orders are graphically depicted, demonstrating thefractional solutions’ closeness to actual data. Analysis of 3D and 2D fractional order graphs reveals convergencetoward integer order graphs as fractional derivatives approach non-fractional ones. This method shows promise fordirect application in solving targeted problems and can be easily adapted for other fractional nature problems.

All Road User Casualties (Killed) in Great Britain from 1926. Linear and Nonlinear Trends with Persistent Data

This paper deals with the analysis of road casualties in Great Britain, using annual data since 1926. Based on the persistent nature of the data, fractional integration methods are used that include linear and non-linear (structural breaks) models. The results indicate that when the whole data set is employed the series is nonstationary I(1) implying permanency of shocks. However, considering data starting in 1964 we observe a significant negative time trend along with a lower degree of integration that implies transitory shocks. In order to avoid the abrupt change produced by the break, a nonlinear deterministic trend model based on Chebyshev polynomials in time is also considered with the whole sample, and though the order of integration is much lower than 1, the unit root null hypothesis cannot yet be rejected.

Fractional accumulative calibration-free odds (f-aCFO) design for delayed toxicity in phase I clinical trials.

The calibration-free odds (CFO) design has been demonstrated to be robust, model-free, and practically useful but faces challenges when dealing with late-onset toxicity. The emergence of the time-to-event (TITE) method and fractional method leads to the development of TITE-CFO and fractional CFO (fCFO) designs to accumulate delayed toxicity. Nevertheless, existing CFO-type designs have untapped potential because they primarily consider dose information from the current position and its two neighboring positions. To incorporate information from all doses, we propose the accumulative CFO (aCFO) design by utilizing data at all dose levels similar to a tug-of-war game where players distant from the center also contribute their strength. This approach enhances full information utilization while still preserving the model-free and calibration-free characteristics. Extensive simulation studies demonstrate performance improvement over the original CFO design, emphasizing the advantages of incorporating information from a broader range of dose levels. Furthermore, we propose to incorporate late-onset outcomes into the TITE-aCFO and f-aCFO designs, with f-aCFO displaying superior performance over existing methods in both fixed and random simulation scenarios. In conclusion, the aCFO and f-aCFO designs can be considered robust, efficient, and user-friendly approaches for conducting phase I trials without or with late-onsite toxicity.

Calculating quasinormal modes of extremal and nonextremal Reissner-Nordström black holes with the continued fraction method

Calculating quasinormal modes of extremal and nonextremal Reissner-Nordström black holes with the continued fraction method