Mathematical Fitting Research Articles

Float Photovoltaic Module Prototype: Design, Simulation, and Electrical Performance Analysis

Photovoltaic solar energy is an abundant, renewable, and clean source of energy that can contribute to the energy transition. However, traditional land-based solar installation have limitations in terms of space, efficiency, and environmental impact. Floating solar panels have emerged as a promising technology that can overcome these limitations and provide a range of benefits. This work describes the design and experimental testing of a small-scale of floating photovoltaic module prototype, with a focus on the effect of solar irradiation on its maximum power output. The prototype is composed of a 4Wp photovoltaic module and a buoyant supporting structure. Using Matlab®, simulations were performed on the floating photovoltaic module under varying environmental conditions, including solar irradiance, temperature, and wind speed. The prototype demonstrated an electrical performance of 3.62W under solar irradiation of 895W/m2 and a temperature of 41°C, with a power ratio exceeding 97% of this maximum power under standard conditions. The prototype also showed a positive energy gain when compared to the same photovoltaic module in a horizontal or inclined position, particularly at high temperature and solar irradiance. Moreover, shows a stability and resistance in harsh weather conditions. The mathematical fitting with a Gaussian distribution shows the rapid increase of the maximum power of the floating photovoltaic module in the range of 37°C to 42°C of temperature with increasing solar irradiance.

Experimental and meso-scale investigation of size effect on fracture properties in three-point concrete beams (TPB)

In this study, the size effect on concrete fracture parameters has been investigated in three distinct groups. While the geometry is similar across each group, the span-to-height ratio varies among the three groups. The study investigates the impact of three different span-to-height ratios (1.85, 2.65, and 4) and five different notch-to-beam height ratios (0.1, 0.2, 0.3, 0.4, and 0.5) by using three-point notched beams (TPB). Beams with identical spans but different heights are used. A new method is proposed to determine the fracture properties of concrete based on the Boundary Effect Method (BEM). A proposed formula for the fictitious cracks is presented based on the results of numerical analyses at the mesoscale and used in the BEM to determine the values of tensile strength and fracture toughness with the effects of span-to-height ratio. The established mesoscale fracture model reproduces the load-displacement curves of 3 PB specimens concrete, which verifies the rationality of the model with the experimental results. Numerical simulation reveals that the fictitious crack length in concrete is highly sensitive to the size of aggregates, their distribution and spacemen’s dimensions. Discussion on BEM based on principles of mathematical fitting and data processing is provided for more objective quasi-brittle fracture experiments and modeling. The size effect law (SEL) is limited by its requirement for sample geometries to be similar, which introduces some additional error when applied to samples with dissimilar geometries. To minimize this error, this study proposes a new formulation within the BEM method. It is found that the fracture parameters predicted by the BEM method using the proposed formulation for different geometries are consistent with the size effect law (SEL) for similar geometries.

Enhanced-release of phenolic-enriched grape seed antioxidants through innovative cholesterol doped phytosomes

Grape seed (GS) is a predominant food by-product in the wine industry and a valuable source of antioxidants due to its high content of polyphenols and fiber. This study aimed to develop an antioxidant-rich GS fraction and formulate appropriate delivery systems for oral administration. A hydroethanolic extract of GS was enriched in phenolic compounds using adsorbent resin column chromatography, resulting in a 4-fold increase in phenolic content compared to the crude extract. The phenolic-enriched fraction was loaded into cholesterol-incorporated phytosomes to improve stability, gut absorption, and oral bioavailability. Different polysaccharide-based polymers were tested as natural-based coatings to improve stability and protection against gastrointestinal degradation while providing a modified-release profile. The phytosomes were evaluated for product yield, particle size, surface charge, surface morphology, and release profile under simulated gastrointestinal conditions. Cholesterol-incorporated phytosomes exhibited an anionic surface charge and a mean hydrodynamic particle size of 168 nm. Both molecular docking and FTIR analyses confirmed the interaction between the lipid bilayer and phenolic compounds. Mathematical fitting models confirmed the modified release profile of the polysaccharide-coated phytosomes. Our enriched phytosomes have potential as smart nutraceuticals for dietary supplements.

A Lifetime Prediction Method of Pressured Gas Polyethylene Pipes by Strain-Hardening Modulus and Tensile Test

In recent years, polyethylene (PE) pipes have been widely utilized for urban natural gas transmission. However, as the use of high-density polyethylene (HDPE) pipes increases, their service life and long-term performance assessment have become one of the most significant issues to be addressed. There has been a ton of studies on PE pipe life prediction techniques both domestically and internationally, but very little has been carried out on PE pipe life prediction in actual gas working environments with varying acid and alkaline levels. This experiment accelerates the aging of PE pipes using acid and alkaline corrosion immersion experiments to determine the lifespan of PE pipes. This study aims to investigate the performance changes of HDPE under strong, weak, and neutral corrosion conditions using corrosion solutions with PH values of 1, 5, and 8, to propose the impact of corrosion caused by various acids and alkalies on the HDPE aging life for natural gas, and to develop a mathematical model between the aging life of polyethylene and the PH values of acid and alkali corrosion solutions. The studies involved soaking and corroding HDPE pipes with various acidity and alkalinity chemicals to speed up the aging process, and then the tensile test was used to determine the mechanical characteristics of the aged PE pipes. Based on our findings, the empirical equation between acidity and service life of PE pipes is obtained by the mathematical fitting method, and a life prediction model of buried city gas HDPE pipes is proposed. The actual life of the aged pipes is determined by the relationship between strain-hardening (SH) modulus and aging time. The findings demonstrate that the service life of PE pipes changes with different levels of acidity and alkalinity: 1.872 days, 1060.507 days, and 1128.58 days following corrosive solution-accelerated aging with solution acidities of PH1, PH5, and PH8, respectively. The life prediction method applies to various plastic pipes in comparable environments as well as HDPE city gas pipes that are subject to acid and alkali corrosion forces.

Experimental and numerical characterization of EPS using elastoplastic response in ABAQUS

Expanded polystyrene (EPS) is an attractive research area in the field of construction engineering. Its ultra-lightweight properties, high compressibility, and environmental-friendly characteristics make it ideal for the use as a compressible backfilling material for embankments, a filling material behind retaining walls and many other applications. Consequently, the compressive strength is one of the important properties for engineers. To this end, this paper aims to create a simplified elastoplastic model for the uniaxial unconfined compressive behavior of EPS. The developed model can predict the plastic stress–strain behavior of EPS using only its elastic modulus. A mathematical curve fitting model was developed by testing several 50 × 50 × 50 mm cube specimens under the test setup of a 50 kN uniaxial loading machine. Then, the proposed model was validated through the elastoplastic behavior in ABAQUS, by creating a finite element model for the described test setup. It was found that the proposed experimental test setup resulted in reasonable stress–strain behavior for EPS, similar to that indicated in the literature. Also, the presented mathematical model can accurately predict the stress–strain behavior of EPS, which was validated using the elastoplastic response in ABAQUS.

Study on the preparation method of porous membranes with single pore size distribution and tailored pore sizes by the induced swelling effect of pre-set graft side chains

To improve the sieving accuracy of material separation, it is necessary to develop a porous membrane with tailored pore size and narrow pore size distribution. Polyvinylidene fluoride (PVDF), the mainstream membrane material, is a semi-crystalline polymer. On the basis of the high elastic state of the PVDF molecular chain in the amorphous region at room temperature, a novel method was proposed to prepare porous membranes with single pore size distribution and tailored pore sizes in this paper. First, 1,3-bis (tris(hydroxymethyl)methylamino) propane (Bis-Tris propane) was grafted onto the PVDF-CTFE main chain during casting solution preparation, and the membranes with the thin and nonporous skin layers were prepared by non-solvent-induced phase separation (NIPS), which had almost no water flux. The membrane with the nonporous skin layer produced a water flux of 35.3 L ∙ m−2∙ h−1∙ bar−1 after soaking in the alkaline glycine solution. FTIR and EDX tests demonstrated that small molecular glycine can be guided into the membrane matrix by the affinity with the polar groups on the pre-set side chains, inducing the reactive swelling effect, which led to the formation of new through holes. Subsequently, the membrane with the nonporous skin layer was initially soaked in ethanol to form pores in advance, then the induced reactive swelling of pre-set graft side chains was carried out. The water flux of obtained membrane was significantly up to 96.9 L ∙ m−2∙ h−1∙ bar−1, proving that the pre-pore forming process successfully strengthened the reactive swelling-caused pore generation effect. Furthermore, based on the enhanced swelling-caused pore generation strategy, amino acids with different molecular sizes were induced to the reactive swelling effect in the amorphous regions. The mathematical fitting showed a linear correlation between the average pore size of the membrane and the molar hydration volume of amino acids, and the membrane was single pore size distribution, verifying that controllably tailored membrane pore size can be realized by the reactive swelling effect of the reactive small molecule with different molecular sizes. Compared to some membranes with single pore size distribution prepared by track etching and anodic oxidation method, the membranes prepared by this method had higher water flux. The water contact angle result clarified that the membrane surfaces and pore channels had excellent hydrophilicity. The reactive swelling did not change the crystallinity and porosity, so the mechanical strength of the membrane did not deteriorate.

Population-wide analysis of hospital laboratory tests to assess seasonal variation and temporal reference interval modification

We identified mortality-, age-, and sex-associated differences in relation to reference intervals (RIs) for laboratory tests in population-wide data from nearly 2 million hospital patients in Denmark and comprising more than 300 million measurements. A low-parameter mathematical wave-based modification method was developed to adjust for dietary and environment influences during the year. The resulting mathematical fit allowed for improved association rates between re-classified abnormal laboratory tests, patient diagnoses, and mortality. The study highlights the need for seasonally modified RIs and presents an approach that has the potential to reduce over- and underdiagnosis, affecting both physician-patient interactions and electronic health record research as a whole.

Superior sensitive, high-tensile flexible fabric film strain sensor

Developing strain sensor with higher sensitivity and larger monitoring range is urgently needed for meeting the increasing potential applications of high-performance sensors in intelligent electronics, motion signal analysis and human monitoring. Herein, via an advanced and efficient method about embedding silver nanowires on electrospun thermoplastic polyurethane fabric film modified with carbon black, a high-performance flexible strain sensor is fabricated. The strain sensor exhibits excellent electrical response abilities of the superior sensitivity (gauge factor >16,000) with strain of 360%, an ultra-wide strain range (0.1% to 200%) and outstanding durability and reliability (>10,000 cycles) under cyclic stretching-recovering operating. Furthermore, mathematical fitting models about variation of resistance (ΔR/R0) and gauge factor upon the applied strains during the stretching process are proposed, which can quantitatively describe and analysis the variation of conductive pathways and inter-particles distance under the external stimuli. It is expected that such fitting models can be used to predict conductive sensing behaviors of flexible strain sensors for actual manufacturing and improvement of products.

Experimental and Numerical Study on the Residence Time Distribution in a Stirred Membrane Reactor

The residence time distribution (RTD) of a reactor is a key factor related to the actual reaction time of reactants, by which the mixing in a reactor can be judged indirectly. Though many efforts have been made to study RTD in stirred tank reactors (STs) or membrane modules, research on RTD in a stirred membrane reactor (SMR) is still lacking. For this purpose, we investigated the influence of operating conditions on mixing in the SMR through experiments, obtained non-ideal mixing region by mathematical model fitting, and analyzed the flow field combined with CFD simulation. The critical value of the ratio of the discharge of impeller to the flow rate is 13.13 designed to reach ideal mixing in the SMR and that of the ratio of the mean residence time to the mixing time is 10 correspondingly. In addition, the RTD is independent of membrane permeability resistance.

Gaussian Model of Anti-Radar Properties for Coatings Based on Carbonyl Iron Powder.

The article presents the Gaussian model of the electromagnetic radiation attenuation properties of two resin systems containing 75% or 80% of a carbonyl iron load as an absorber in the 4-18 GHz range. For the attenuation values obtained in the laboratory, mathematical fitting was performed in the range of 4-40 GHz to visualize the full curve characteristics. The simulated curves fitted up to a 0.998 R2 value of the experimental results. The in depth analysis of the simulated spectra allowed a thorough evaluation of the influence of the type of resin, absorber load, and layer thickness on reflection loss parameters such as the maximum attenuation, peak position, half-height width, and base slope of the peak. The simulated results were convergent with the literature findings, allowing a much deeper analysis. This confirmed that the suggested Gaussian model could provide additional information, useful in terms of comparative analyses of datasets.

A Novel Strategy for Comprehensive Estimation of Lattice Energy, Bulk Modulus, Chemical Hardness and Electronic Polarizability of ANB8-N Binary Inorganic Crystals

How to search for a convenient method without a complicated calculation process to predict the physicochemical properties of inorganic crystals through a simple micro-parameter is a greatly important issue in the field of materials science. Herein, this paper presents a new and facile technique for the comprehensive estimation of lattice energy (U), bulk modulus (B), chemical hardness (ƞ), and electronic polarizability (α), just by using a simple mathematic fitting formula with a few structure parameters, such as the systems of rock salt crystals (group I–VII, II–VI) and tetrahedral coordinated crystals (group II–VI, III–V). For the typical binary ANB8-N crystal systems, our present conclusions suggest that a good quantitative correlation between U, B, ƞ, α and chemical bond length (d) is observed, the normal mathematical expression is P = a·db (P represents these physicochemical parameters), constants a and b depend on the type of crystals, and the relevant squares of the correlation coefficient (R2) are larger than 0.9. The results indicate that lattice energy, bulk modulus, and chemical hardness decrease with increases in chemical bond length, but electronic polarizability increases with an increase in chemical bond length. Meanwhile, the new data on the lattice energy, bulk modulus, chemical hardness, and electronic polarizability values of binary ANB8-N crystal systems considered in the present study are calculated via the obtained curve fitting equations without any complex calculation process. We find that there is a very good linear trend in our calculated results along with the values reported in the literature. The present study will be important in solid-state chemistry, which may give researchers useful guidance in searching for relevant data for predicting the properties of new materials or synthetic routes based on a simple mathematic empirical model.

Machine learning-aided characterization of microbubbles for venturi bubble generator

The characterization of microbubbles for venturi tube is important for the associated industrial applications, but still challenging due to the coupling effects of numerous operating factors. Here, we report a machine learning (ML)-aided approach for predicting the characteristics of microbubbles generated by venturi tube. Full factorial design of experiments (DOE) was first carried out, followed by the image post-processing to obtain multi-dimensional dataset. After data cleaning, MLP (Multi-Layer Perception), random forest (RF) and Catboost models were trained to correlate the Sauter mean diameter (ds) to five operating features, namely, throat-to-outlet ratio β, divergent angle θ, gas-to-liquid ratio α, gas Reynolds number Reg and liquid Reynolds number Rel. All three ML models provide excellent predictability on ds, while the Catboost model displays the best extrapolation performance in three investigated scenarios. Internal importance analysis shows that the throat size and Reg play the greatest and least influence on ds, respectively. We also explored the mathematical fitting approach based on obtained experimental dataset. The results show that ML models deliver improved predictive performance over mathematical model, but the latter provides better mechanistic interpretability. This work demonstrates the great potential of ML in the gas–liquid multiphase flow.

Effect of slope shape on soil aggregate stability of slope farmland in black soil region

Slope erosion in the black soil region of Northeast China is complex and specific. In order to effectively control soil erosion and protect scarce black soil resources, it is necessary to reveal the law of soil erosion and the influence of basic units of soil structure on its erosion process. This paper used three treatments in the Le Bissonnais (LB) method to determine soil aggregate stability parameters and soil erodibility K values based on particle size composition. By establishing a mathematical fitting of the slope erosion rate along the slope length, it is found that the sinusoidal function fitting can better characterize the periodic law of the slope erosion rate of the long and gentle slope cultivated land in the typical black soil region. The research shows that the primary mechanism of black soil aggregate breakage is dissipation and mechanical disturbance, while the damage caused by clay expansion is the least.

Prediction of growth performance parameters in the growing and free-range finishing phases of the Iberian pig via meta-analysis

Aim of study: To describe and predict mathematically the growth parameters of Iberian pigs. Area of study: Iberian dehesa agroforestry system. Southwest of Iberian Peninsula. Material and methods: A quantitative and systematic review was carried out to find all studies with valid data of growth and finishing in the Iberian swine breed published up to May 2020. For the analysis of the data, a mathematical fitting model was obtained and a function was postulated to describe the relation between the variables age and body weight. Main results: 112 publications were found, and after applying several quality filters, 18 with age and weight matched data were used. The database was composed of 76 different tests and 22,558 animals. The clasical growth phases were independently evaluated for data analysis.It was necessary to separate the finishing trials into three groups according to the starting age. Seven mathematical models were obtained for lactation,post-weaning, and montanera finishing. However, no valid test data were found during the growth and prefinishing phases. Besides that, a single model was obtained combining lactation and post-weaning, and another surface model including the variables age and weight to compare average daily weight gain in montanera finishing phase. Research highlights: After systematic review of the studies that provide information on the growth of Iberian pigs, and a quantitative analysis, some mathematical linear and nonlinear models have been developed for the prediction of the production ratios at different phases.

Shock Vibration Control of SDOF Systems with Tubular Linear Eddy Current Dampers

The nonlinear dynamic characteristic of a tubular linear eddy current damper (TLECD) and the transient responses to shock excitations of a single-degree-of-freedom (SDOF) system with the TLECD are studied. First, the nonlinear force-velocity relationship of the TLECD is discussed using the finite element simulation and mathematical model fitting. Next, the influences of three forms of shock excitation and various mechanical parameters of the TLECD on shock vibration control of an SDOF system with the TLECD are investigated. Moreover, for the SDOF systems with the TLECD or the nonlinear fluid viscous dampers (FVD) at the same maximum displacement and maximum damper force, the time to reach the maximum displacement, the time to reach one-third of the maximum displacement, the energy input of the external loading, and the energy dissipation of dampers are analyzed and compared. Finally, the shock response spectrums (SRSs) of the SDOF system and the design flowchart for the TLECD are presented to provide a reference for shock vibration control of the SDOF system with the nonlinear TLECD and the design of TLECDs. The results show that there is an optimal dimensionless critical relative velocity that minimizes the dimensionless maximum damping force for reaching the target maximum displacement, and compared to the FVD, the TLECD greatly shortens the time to reach one-third of the maximum displacement.

Numerical study on erosion behavior of sliding sleeve ball seat for hydraulic fracturing based on experimental data

The sleeve sealing ball seat is one of the important components in the multistage fracturing process of horizontal wells. The erosion and wear of the surface will decrease the sealing performance of the fracturing ball and the ball seat. This leads to pressure leakage during the fracturing process and fracturing failure. In this paper, combined with the actual ball seat materials and working conditions during the fracturing process, the erosion tests of ductile iron and tungsten carbide materials under different erosion speeds, angles, and mortar concentrations are carried out. Then the erosion test results were analyzed by mathematical fitting, and a set of erosion models suitable for sliding sleeve setting ball seat materials were innovatively established. For the first time, this paper combines the erosion model obtained from the experiment and the computational fluid dynamics (CFD) with Fluent software to simulate the erosion of the ball seat. Based on the simulation results, the morphology of the sliding sleeve seat ball after erosion is predicted. Through analysis of the test and simulation results, it is showed that the erosion rate of tungsten carbide material is lower and the wear resistance is better under the condition of small angle erosion. This research can offer a strong basis for fracturing site selection, surface treatment methods, and prediction of failure time of ball seats.

Predicting the Glycemic Index of Biscuits Using Static In Vitro Digestion Protocols.

In vitro digestion methods that can accurately predict the estimated GI (eGI) values of complex carbohydrate foods, including biscuits, are worth exploring. In the current study, standard commercial biscuits with varied clinical GI values between 9~30 were digested using both the INFOGEST and single-enzyme digestion protocols. The digestion kinetic parameters were acquired through mathematical fitting by mathematical kinetics models. The results showed that compared with the INFOGEST protocol, the AUR180 deduced from digesting using either porcine pancreatin or α-amylase showed the best potential in predicting the eGI values. Accordingly, mathematical equations were established based on the relations between the AUR180 and the GI values. When digesting using porcine pancreatin, GI= 1.834 + 0.009 ×AUCR180 (R2= 0.952), and when digesting using only α-amylase, GI= 6.101 + 0.009 ×AUCR180 (R2=0.902). The AUR180 represents the area under the curve of the reducing-sugar content normalized to the total carbohydrates versus the digestion time in 180 min. The in vitro method presented enabled the rapid and accurate prediction of the eGI values of biscuits, and the validity of the formula was verified by another batch of biscuits with a known GI, and the error rate of most samples was less than 30%.

Crater effects of shallow burial explosions in soil based on SPH-FEM analysis

This study analyzed the effects and influencing factors of shallowly-buried explosions in soil based on the design and implementation of static explosion experiments and numerical simulations. Based on the static explosion test data, a numerical analysis model of SPH-FEM was established and the explosion process and pit parameters in explosions shallowly buried in soil were analyzed. The results of numerical calculations and comparisons verified the effectiveness of the SPH-FEM method in simulating shallowly-buried explosions in soil. Furthermore, the similarities and differences between the SPH-FEM and ALE methods in the numerical simulation of the same explosion in the soil were assessed. The relationships between the blasting pit radius and explosive depth, and between the explosives weight and pit volume were analyzed. The empirical curve formula of the explosive depth and the crater radius with 9.35 kg of TNT explosive were obtained by mathematical fitting. The results showed that the SPH-FEM method was more refined and more computationally efficient than the ALE method to simulate shallow burial explosions in soil. The established empirical curve formula, which expressed the relationship between the explosive burial depth and the pit radius, effectively predicted the pit radius of the shallow burial explosion. With increasing explosive burial depth, the pit radius increased to the peak value and then decreased rapidly.

Synthesis of guar gum-g-coconut husk (SnO<SUB align="right">2-SiO<SUB align="right">2) nanocomposite for removal of Cu (II) and Cr (VI) from wastewater

A new sorbent material namely 'guar gum-g-coconut husk (SnO2-SiO2) [GG-g-CH(SnO2-SiO2)] nanocomposite' was synthesised by preparation of coconut husk metal oxide nanoparticles and grafted into acrylamide modified guar gum (GG) base with the help of crosslinking agent glutaraldehyde. Its adsorption capacity was evaluated for the adsorption of Cu (II) and Cr (VI) metal ions from wastewater and factors affecting variables such as pH, adsorbent dose, contact time, and concentration were extensively investigated. It was found from the study that the maximum percent removal achieved was 99% for Cu (II) and 92.74% Cr (VI) at a pH of 8.3 and 7.2 respectively with an optimum adsorbent dose of 250 mg/l in 120 mins. The sorption data obeyed both Langmuir and Freundlich isotherms but Freundlich isotherm was better mathematical fit than Langmuir model. The Langmuir sorption capacity (qmax) was found to be 105.26 and 98.03 mg/g for Cu (II) and Cr (VI) respectively. Freundlich constants, KF values obtained for Cu (II) was 1.135 and for Cr (VI) was 1.11 while 1/n values obtained for Cu (II) was 0.647 and for Cr (VI) was 0.656, respectively.

Reliability of HCT-based Soil Water Retention Curves

The measurement of SWRCs using HCTs has been the subject of several recent studies. Consequently, there have been several design and experimental procedures developed. However, despite these developments, the accuracy, range and duration of HCT-based measurement is still largely characterized by uncertainties and inconsistencies, thereby, reducing the reliability of the obtained SWRCs. In this work, an experimental program is designed to address these uncertainties. SWRCs of reconstituted London clay were measured using the continuous drying method with evaporation rate control. The obtained SWRCs were analysed based on the maximum suction value recorded by HCTs (smax), the obtained air-entry value (saev), the suction at inflection point (si), the water content at inflection point (wi), and the slope of tangent to inflection point (mi). A percentage uncertainty of ±4% was obtained for the saev and si values. Similarly, percentage uncertainties of ±6% and ±0.5% were obtained respectively for the mi and wi values. These results were further compared with parametric analysis of the reported SWRCs of the same soil in the literature. Given the observed tolerance ranges, cautions must be taken in selecting values for these parameters e.g. as input values in mathematical curve fitting equations for prediction of the entire SWRC, or in unsaturated constitutive modelling, to enhance reliability of the outputs.