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.

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.

Influence of MnO_2 modification methods on the catalytic performance of CuO/CeO_2 for NO reduction by CO

In order to investigate the influence of MnO2 modification methods on the catalytic performance of CuO/CeO2 catalyst for NO reduction by CO, two series of catalysts （xCuyMn/Ce and xCu/yMn/Ce） were prepared by co-impregnation and step- wise-impregnation methods, and characterized by means of X-ray diffraction （XRD）, Raman spectra, H2-temperature programmed reduction （H2-TPR）, in situ diffuse reflectance infrared Fourier transform spectra （in situ DRIFTS） techniques. Furthermore, the cata- lytic performances of these catalysts were evaluated by NO＋CO model reaction. The obtained results indicated that： （1） The catalysts acquired by co-impregnation method exhibited stronger interaction owing to the more sufficient contact among each component of the catalysts compared with the catalysts obtained by stepwise-impregnation method, which was beneficial to the improvement of the reduction behavior; （2） The excellent reduction behavior was conducive to the formation of low valence state copper species （Cu＋/Cu0） and more oxygen vacancies （especially the surface synergetic oxygen vacancies （SSOV, Cu＋-n-Mn（4-x）-）） during the reaction process, which were beneficial to the adsorption of CO species and the dissociation of NO species, respectively, and further promoted the en- hancement of the catalytic performance. Finally, in order to further understand the difference between the catalytic performances of these catalysts prepared by co-impregnation and stepwise-impregnation methods, a possible reaction mechanism （schematic diagram） was tentatively proposed.

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.

The chance of sodium titanate anode for the practical sodium-ion batteries

Supporting sustainable green energy systems,there is a big demand gap for grid energy storage.Sodiumion storage,especially sodium-ion batteries(SIBs),have advanced significantly and are now emerging as a feasible alternative to the lithium-ion batteries equivalent in large-scale energy storage due to their natural abundance and prospective inexpensive cost.Among various anode materials of SIBs,beneficial properties,such as outstanding stability,great abundance,and environmental friendliness,make sodium titanates(NTOs),one of the most promising anode materials for the rechargeable SIBs.Nevertheless,there are still enormous challenges in application of NTO,owing to its low intrinsic electronic conductivity and collapse of structure.The research on NTOs is still in its infancy;there are few conclusive reviews about the specific function of various modification methods.Herein,we summarize the typical strategies of optimization and analysis the fine structures and fabrication methods of NTO anodes combined with the application of in situ characterization techniques.Our work provides effective guidance for promoting the continuous development,equipping NTOs in safety-critical systems,and lays a foundation for the development of NTO-anode materials in SIBs.

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.

Output-only identification of the modal and physical properties of structures using free vibration response

The viability of a complete structural characterization of civil structures is explored and discussed. In particular, the identification of modal （i.e. natural frequencies, damping ratios and modal shapes） and physical properties （i.e. mass and stiffness） using only the structure＇s free decay response is studied. To accomplish this, modal analysis from flee vibration response only （MAFVRO） and mass modification （MM） methodologies are engaged along with Wavelet based techniques for optimal signal processing and modal reconstruction. The methodologies are evaluated using simulated and experimental data. The simulated data are extracted from a simple elastic model of a 5 story shear building and from a more realistic nonlinear model of a RC frame structure. The experimental data are gathered from shake table test of a 2-story scaled shear building. Guidelines for the reconstruction procedure from the data are proposed as the quality of the identified properties is shown to be governed by adequate selection of the frequency bands and optimal modal shape reconstruction. Moreover, in cases where the structure has undergone damage, the proposed identification scheme can also be applied for preliminary assessment of structural health.

Afteruse development of former landfll sites in Hong Kong

Landfll is one of the major methods in disposing of municipal solid waste(MSW) in Hong Kong. There are now 13 closed landfll sites in Hong Kong, and a restoration program has been launched since 1999 to transform the closed landfll sites back into recreational area. The MSW underneath these closed landfll sites will biodegrade slowly and gradually, releasing toxic gases and leachate. As there have only been a few afteruse development ever completed in Hong Kong, this paper describes the consideration in planning and design of two former landfll sites in Hong Kong–Ngau Chi Wan(NCW) and Jordan Valley(JV) landflls, in particular a discussion on the MSW settlement. Various models in predicting the longterm MSW settlement have been available. This paper reviews the applicability of these models to predict MSW settlement. However, as the predicted settlements can be signifcantly in error, they need sitespecifc calibration and validation. This paper therefore presents the settlement monitoring data in these former landfll sites over the last 30 years, and suggests modifying the Bjarngard and Edgers’ method for estimating this long-term settlement as well as the effect of additional surcharge due to afteruse development. Based on the regression of these data, compression indices Cce and C at different stages of the settlement in the modifed method have been calibrated and validated.

Recent advances on bismuth oxyhalides for photocatalytic CO_(2)reduction

Photocatalytic conversion of CO_(2)into fuels such as CO,CH_(4),and CH_(3)OH,is a promising approach for achieving carbon neutrality.Bismuth oxyhalides(BiOX,where X=Cl,Br,and I)are appropriate photocatalysts for this purpose due to the merits of visible-light-active,efficient charge separation,and easy-to-modify crystal structure and surface properties.For practical applications,multiple strategies have been proposed to develop high-efficiency BiOX-based photocatalysts.This review summarizes the development of different approaches to prepare BiOX-based photocatalysts for efficient CO_(2)reduction.In the review,the fundamentals of photocatalytic CO_(2)reduction are introduced.Then,several widely used modification methods for BiOX photocatalysts are systematacially discussed,including heterojunction construction,introducing oxygen vacancies(OVs),Bi-enrichment,heteroatom-doping,and morphology design.Finally,the challenges and prospects in the design of future BiOX-based photocatalysis for efficient CO_(2)reduction are examined.

Factors affecting thermal stability of collagen from the aspects of extraction,processing and modification

Collagen,as a thermal-sensitive protein,is the most abundant structural protein in animals.Native collagen has been widely applied in various fields due to its specific physicochemical and biological properties.The beneficial properties would disappear with the collapse of the unique triple helical structure during heating.Understanding thermal stability of collagen is of great significance for practical applications.Previous studies have shown the thermal stability would be affected by the different sources,extraction methods,solvent systems in vitro and modified methods.Accordingly,the factors affecting thermal stability of collagen are discussed in detail in this review.

Chemisorption solid materials for hydrogen storage near ambient temperature:A review

Solid chemisorption technologies for hydrogen storage,especially high-efficiency hydrogen storage of fuel cells in near ambient temperature zone defined from−20 to 100℃,have a great application potential for realizing the global goal of carbon dioxide emission reduction and vision of carbon neutrality.However,there are several challenges to be solved at near ambient temperature,i.e.,unclear hydrogen storage mechanism,low sorption capacity,poor sorption kinetics,and complicated synthetic procedures.In this review,the characteristics and modification methods of chemisorption hydrogen storage materials at near ambient temperature are discussed.The interaction between hydrogen and materials is analyzed,including the microscopic,thermodynamic,and mechanical properties.Based on the classification of hydrogen storage metals,the operation temperature zone and temperature shifting methods are discussed.A series of modification and reprocessing methods are summarized,including preparation,synthesis,simulation,and experimental analysis.Finally,perspectives on advanced solid chemisorption materials promising for efficient and scalable hydrogen storage systems are provided.

EXACT SOLUTIONS TO KdV-BURGERS EQUATION USING THE ENHANCED MODIFIED SIMPLE EQUATION METHOD

It is known that many physical phenomenons can be described by the KdV-Burgers equation. By the enhanced modifed simple equation method, we obtain the exact solutions with variable coefcients involving parameters to KdV-Burgers equation, and some new exact solutions are gained. When these parameters are taken special values, the solitary wave solutions are derived from the exact solutions. It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.