Adomian Modification Methods for the Solution of Chebyshev’s Differential Equations

The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.

Selecting the Technology of Sodium Silicate Modified Poplar with the Highest Performance by Fuzzy Orthogonal Method

Sodium silicate modification can improve the overall performance of wood.The modification process has a great influence on the properties of modified wood.In this study,a new method was introduced to analyze the wood modification process,and the properties of modified wood were studied.Poplar wood was modified with sodium silicate by vacuum-pressure impregnation.After screening using single-factor experiments,an orthogonal experiment was carried out with solution concentration,impregnation time,impregnation pressure,and the cycle times as experimental factors.The modified poplar with the best properties was selected by fuzzy mathematics and characterized by SEM,FT-IR,XRD and TG.The results showed that some lignin and hemicellulose were removed from the wood due to the alkaline action of sodium silicate,and the orderly crystal area of poplar became disorderly,resulting in the reduction of crystallinity of the modified poplar wood.FT-IR analysis showed that sodium silicate was hydrolyzed to form polysilicic acid in wood,and structural analysis revealed the formation of Si-O-Si and Si-O-C,indicating that sodium silicate reacted with fibers on the wood cell wall.TG-DTG curves showed that the final residual mass of modified poplar wood increased from 25%to 67%,and the temperature of the maximum loss rate decreased from 343℃ to 276℃.The heat release and smoke release of modified poplar wood decreased obviously.This kind of material with high strength and fire resistance can be used in the outdoor building and indoor furniture.

Statistical Modification Analysis of Helical Planetary Gears based on Response Surface Method and Monte Carlo Simulation

Tooth modification technique is widely used in gear industry to improve the meshing performance of gearings. However, few of the present studies on tooth modification considers the influence of inevitable random errors on gear modification effects. In order to investigate the uncertainties of tooth modification amount variations on system＇s dynamic behaviors of a helical planetary gears, an analytical dynamic model including tooth modification parameters is proposed to carry out a deterministic analysis on the dynamics of a helical planetary gear. The dynamic meshing forces as well as the dynamic transmission errors of the sun-planet 1 gear pair with and without tooth modifications are computed and compared to show the effectiveness of tooth modifications on gear dynamics enhancement. By using response surface method, a fitted regression model for the dynamic transmission error（DTE） fluctuations is established to quantify the relationship between modification amounts and DTE fluctuations. By shifting the inevitable random errors arousing from manufacturing and installing process to tooth modification amount variations, a statistical tooth modification model is developed and a methodology combining Monte Carlo simulation and response surface method is presented for uncertainty analysis of tooth modifications. The uncertainly analysis reveals that the system＇s dynamic behaviors do not obey the normal distribution rule even though the design variables are normally distributed. In addition, a deterministic modification amount will not definitely achieve an optimal result for both static and dynamic transmission error fluctuation reduction simultaneously.

Modification Design Method for an Enveloping Hourglass Worm Gear with Consideration of Machining and Misalignment Errors

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

Study on Modification Mechanism of Rare Earth in ZA27 Cast Alloy with Electronic Theory and Molecular Dynamics Method

A model of liquid ZA27 cast alloy is established according to molecular dynamics theory and an atomic structural model of co-existent a phase and liquid is also presented by means of computer programming. Recursion method is adopted to calculate the electronic structure of RE (rare earth) in grains and around phase boundaries respectively. The calculation shows that RE is more stable around phase boundaries than in grains, which explains the fact that the solution of RE in a phase is less, and RE mainly aggregates in front of phase boundary. The calculations of bonding order integrals also show that RE in front of phases hardly solidify onto the grain surfaces as active element so as to prevent grains growth and refine the grains. As a result, the modification mechanism of RE may be explained from the view of electronic structure.

Different surface modification methods and coating materials of zinc metal anode

Rechargeable aqueous Zn-ion batteries(AZIBs)are one of the most promising energy storage devices for large-scale energy storage owing to their high specific capacity,eco-friendliness,low cost and high safety.Nevertheless,zinc metal anodes suffer from severe dendrite growth and side reactions,resulting in the inferior electrochemical performance of AZIBs.To address these problems,surface modification of zinc metal anodes is a facile and effective method to regulate the interaction between the zinc anode and an electrolyte.In this review,the current challenges and strategies for zinc metal anodes are presented.Furthermore,recent advances in surface modification strategies to improve their electrochemical performance are concluded and discussed.Finally,challenges and prospects for future development of zinc metal anodes are proposed.We hope this review will be useful for designing and fabricating highperformance AZIBs and boosting their practical applications.

Peanut proteins:Extraction,modifications,and applications:A comprehensive review

As naturally sourced proteins,peanut proteins have garnered significant attention from the food industry,owing to their numerous advantages,such as easy extraction,non-pungency,and high bioavailability.Furthermore,peanut proteins are highly digestible in the gastrointestinal tract and boast a high net protein utilization rate,making them an appealing protein source in food products and a promising alternative to animal protein.In this paper,the recent works on the extraction method,modification method,and application of peanut proteins were reviewed.Both advantages and disadvantages of current extraction and modification were discussed.Recently updated information about peanut protein research was summarized.Based on these,the prospection of peanut proteins research was presented,which may be instructive for future research in this field.Future research is still needed for accessible modification methods to develop the functional properties of peanut proteins.

New Modification of Fixed Point Iterative Method for Solving Nonlinear Equations

In this paper, we have modified fixed point method and have established two new iterative methods of order two and three. We have discussed their convergence analysis and comparison with some other existing iterative methods for solving nonlinear equations.

Solution of Laguerre’s Differential Equations via Modified Adomian Decomposition Method

This paper presents a technique for obtaining an exact solution for the well-known Laguerre’s differential equations that arise in the modeling of several phenomena in quantum mechanics and engineering. We utilize an efficient procedure based on the modified Adomian decomposition method to obtain closed-form solutions of the Laguerre’s and the associated Laguerre’s differential equations. The proposed technique makes sense as the attitudes of the acquired solutions towards the neighboring singular points are correctly taken care of.

Study on Plasticity Modification for Measuring High Residual Stress by Hole-Drilling Method

Hole-drilling method is a commonly used method for measuring residual stress. The calibration coefficients in ASTM E837-13 a would cause large errors due to the plasticity deformation of materials. In the study, calibration coefficients were modified in the plasticity deformation stage based on the distortion energy theory. The calibration experiment of calibration coefficients was simulated by the finite element model, and the plasticity modification formulas of 7075 aluminum alloy were obtained. From the results of uniaxial tensile loading test, the measuring errors of high residual stress are significantly reduced from-4.071%～53.440% to-5.140% ～ 0.609% after the plasticity modification. This work provides an effective way to expand the application of hole-drilling method.

Newton-type methods and their modifications for inverse heat conduction problems

This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs.

Modification Mechanism of Rare Earth Elements in ZA27 Casting Alloys

The model of the liquid-phase ZA27 alloys was set up by molecular dynamics theory. The atomic structure of phase, RE-compounds, and the phase-liquid interface in ZA27 alloys were constructed by computer programming. Electronic structures of phase with rare earth elements dissolved and of phase-liquid interfaces with rare earth elements enrichment in ZA27 casting alloys were investigated by using the Recursion method. The ESE energy of RE elements and the structure energy of RE-compounds, phase, and the liquid-phase ZA27 alloys were calculated. The results show that rare earth elements are more stable to be in the phase interface than in phase, which explains the fact of very small solid solubility of rare earth elements in phase, and the enrichment in the solid-liquid growth front. This makes dendrite melt and break down, dissociate and propagate. RE-compounds can act as heterogeneous nuclei for phase, leading to phase refinement. All above elucidates the modification mechanism of rare earth elements in zinc-aluminum casting alloys at electronic level.

Electrochemical behavior of Cu-Zn-Al shape memory alloy after surface modification by electroless plated Ni-P

The electrochemical behavior of Cu-Zn-Al shape memory alloy (SMA) with andwithout electroless plated Ni-P was investigated by electrochemical methods, in artificial Tyrode'ssolution. The results showed that Cu-Zn-Al SMA engendered dezincification corrosion in Tyrode'ssolution. The anodic active current densities as well as electrochemical dissolution sensitivity ofthe electroless plated Ni-P Cu-Zn-Al SMA increased with NaCl concentration rising, pH of solutiondecreasing and environmental temperature uprising. X-ray diffraction analysis indicated that aftersurface modification by electroless plated Ni-P, an amorphous plated film formed on the surface ofCu-Zn-Al SMA. This film can effectively isolate matrix metal from corrosion media and significantlyimprove the electrochemical property of Cu-Zn-Al SMA in artificial Tyrode's solution.

Morphological modifications of C60 crystal rods under hydrothermal conditions

We observed morphological modification of rod-shaped C60 solvate crystals using a facile hydrothermal method.The initial C60 rods were changed from smooth rods to rough rods,porous rods or pieces under different hydrothermal conditions.During the hydrothermal treatment,the initial samples underwent a decomposition-recrystallization process,which can be tuned by the content of alcohol in the hydrothermal solution,thereby leading to modification of the morphological properties of the initial C60 rods.In addition,the rough and porous C60 rods prepared in our work exhibit excellent photoluminescence intensities that are approximately 7 and 3 times higher than those of pure C60 powders,respectively.Our results suggest that the hydrothermal method is a potential route for fabricating fullerene materials with controllable morphologies and novel functions.

An Alternative Regression-Based Approach to Estimate the Crash Modification Factors of Multiple Treatments Using Before-and-After Data

Before-and-after methods have been effectively used in the road safety studies to estimate Crash Modification Factors (CMFs) of individual treatments as well as the multiple treatments on roadways. Since the common practice is to apply multiple treatments on road segments, it is important to have a method to estimate CMFs of individual treatment so that the effect of each treatment towards improving the road safety can be identified. Even though there are methods introduced by researchers to combine multiple CMFs or to isolate the safety effectiveness of individual treatment from CMFs developed for multiple treatments, those methods have to be tested before using them. This study considered two multiple treatments namely 1) Safety edge with lane widening 2) Adding 2 ft paved shoulders with shoulder rumble strips and/or asphalt resurfacing. The objectives of this research are to propose a regression-based method to estimate individual CMFs estimate CMFs using before-and-after Empirical Bayes method and compare the results. The results showed that having large sample size gives accurate predictions with smaller standard error and p-values of the considered treatments. Also, results obtained from regression method are similar to the EB method even though the values are not exactly the same. Finally, it was seen that the safety edge treatment reduces crashes by 15% - 25% and adding 2 ft shoulders with rumble strips reduces crashes by 25% - 49%.

Investigation on Instantaneous Meshing Stiffness and Profile Modification of Involute Helical Gear

An efficient finite element model of involute helical gear is presented. A program based on compliance matrix method is developed for the calculation of instantaneous meshing stiffness, and the relationship between the rate of meshing stiffness and overlap ratio is given. On the basis of stiffness calculation, an optimization program for the optimal design of profile modification is developed according to the principle of internal point punishment function method.

Model Simplification and Parameter Modification for Offshore Platforms Using Experiment Data

In this paper, a computation method has been developed so as to compare the finite element method (FEM) with the test results directly. The structure is divided into the 'master' and 'slave' degrees of freedom. The simplified model can be obtained with modal reduction. Then the design sensitivity analysis of the eigenvalues and eigenvectors has been carried out using the modal frequency and modal shape of the test. A two-story frame structure and a jacket model structure have been calculated. Meanwhile, the modified coefficient, the FEM computational and experimental values have been given. It has been shown that the FEM model modified using the test modal value is efficient.

Effects of surface modification by Ni, Ti and B on electrochemical properties of Mg_(1.8)Cu_(0.2)Ni hydrogen storage alloy

Amorphous alloy Mg1.8Cu0.2Ni was successfully prepared by mechanical alloying （MA） and a series of （n-x）Ni- x（Ti＋B） composites were synthesized by MA. The electrochemical properties of Mgl.8Cu0.2Ni coated by Ni, Ti and B were studied by cyclic charge-discharge, linear polarization curve, and hydrogen diffusion coefficient experiments. Experimental results indicate that Mg1.8Cu0.2Ni-[0.9Ni0.6（Ti＋B）] composite which was MA 30 h exhibited the best performance and its initial discharge capacity arrived to 714.1 mAh/g. After 30 cycles the discharge capacity was above 530 mAh/g, which was much higher than that of Mg1.8Cu0.2Ni. And after 100 cycles it holded still 442.1 mAh/g. On all accounts, after modification by Ni, Ti and B, the initial discharge capacity and high-rate discharge ability of the electrode were evidently increased. At the same time, the cycle performance was also improved significantly.

Modification of Classical SPM for Slightly Rough Surface Scattering with Low Grazing Angle Incidence

Based on the impedance/admittance rough boundaries, the reflection coefficients and the scattering cross section with low grazing angle incidence are obtained for both VV and HH polarizations. The error of the classical perturbation method at grazing angle is overcome for the vertical polarization at a rough Neumann boundary of infinite extent. The derivation of the formulae and the numerical results show that the backscattering cross section depends on the grazing angle to the fourth power for both Neumann and Dirichlet boundary conditions with low grazing angle incidence. Our results can reduce to that of the classical small perturbation method by neglecting the Neumann and Dirichlet boundary conditions.

Nanoparticles Modified Electrodes: Synthesis, Modification, and Characterization—A Review

Nanoparticles offer unique features such as a larger surface area and enhanced electrochemical performance compared to their contemporary matters. These properties make them suitable to be considered in bridging the lacunae associated with the use of bare electrodes in electrochemical sensors. Nanomaterials enhance the redox reversibility on the electrodes’ surfaces, hence, improving the reproducibility, sensitivity, and limit of detection of the electrodes/sensors. Their methods of synthesis (top-to-bottom and bottom-to-to-top) are tailored toward manipulating their sizes, shapes, and preventing their agglomeration. This review paper provides a synopsis on research done in synthesizing nanoparticles, modifying electrodes, and pinpointing the improved performances of the modified electrodes via known characteristic techniques, namely: cyclic voltammetry, differential pulse voltammetry, and electrochemical impedance spectroscopy. In addition, a perspective is given in terms of increasing the lifespan of the working electrodes and the need for non-faradaic sensors.