Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and on...Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P2O7 unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs.展开更多
Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions be...Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with a...Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.展开更多
This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensiona...This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.展开更多
Abstract A method of Baotou mixed rare earth concen- trate leaching was investigated. According to the principle of complex leaching, the quadratic orthogonal regression experiment was used to investigate effect of si...Abstract A method of Baotou mixed rare earth concen- trate leaching was investigated. According to the principle of complex leaching, the quadratic orthogonal regression experiment was used to investigate effect of six factors. An optimal condition of low energy and environment friendly was determined as follows: HCl acidity is 4 mol.L-1, AlCl3 concentration is 2 mol.L-l, reaction temperature is 85 ℃, reaction time is 90 rain, liquid to solid ratio is 35 ml.g-1, and stirring speed is 100 r.min-1. According to this condition, the leaching ratio of mixed rare earth con- centrate is 76.5 %. The analyses of X-ray diffraction shows that bastnasite disappears, and the main peaks of filter residue is monazite and cheralite after leaching of HCl- AlCl3 solution. The result indicates that REFCO3 of the mixed rare earth concentrate can be dissolved, but REPO4 remains in the leaching residue. This method provides a way to separate and extract rare earth.展开更多
In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ...In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.展开更多
Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coeffi...Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.展开更多
Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating ...Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating combustion, the desired nanocrystalline perovskite LaMnO3 was obtained and no further calcination was carried out. The possible processes of combustion reaction were discussed according to the principle of propellant chemistry. The autocombustion and thermal decomposition of the precursor were investigated using the TG-DTA and FT-IR techniques. The influences of glycine-nitrate molar ratio and heat-treatment temperature on the perovskite phase formation and crystallite size of as-burnt powder were studied by XRD. The morphology and size of the as-burnt powder before and after milling were characterized and compared by TEM.展开更多
This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmet...This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding (2+1)-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.展开更多
When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the...When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.展开更多
By using the (G'/G)-expansion method and the variable separation method, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is obtained. Based on the derived solitary wave solutions, we o...By using the (G'/G)-expansion method and the variable separation method, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is obtained. Based on the derived solitary wave solutions, we obtain some special localized excitations and study the interactions between two solitary waves of the system.展开更多
Electrospun WO_3 nanofibers were fabricated by coaxial electrospinning and directly annealing WCl_6/polyvinylpyrrolidone(PVP) nanofibers on activated carbon fibres(ACF), and characterized by scanning electron microsco...Electrospun WO_3 nanofibers were fabricated by coaxial electrospinning and directly annealing WCl_6/polyvinylpyrrolidone(PVP) nanofibers on activated carbon fibres(ACF), and characterized by scanning electron microscopy(SEM) and X-ray diffractometry(XRD). The most suitable condition for electrospinning is the mass ratio of WCl_6 to PVP 0.6, appropriate amount DMF and ethanol, a voltage of 28 kV, the reception distance of 15 cm, the humidity range within 10% and 20% and the moving rate of the pump 0.001 mm/s. The photocatalytic activities of WO_3 nanofibers were evaluated by the photo-degradation of phenol solution under the irradiation of 500 W xenon lamp. The results showed that, the sizes of the fibers are about 100 nm, and after being photodegraded for 210 min, the concentration of phenol decreased from 20.05 mg/L to 8.60 mg/L. Thus, the photo-degradation rate of WO_3 nanofibers for phenol solution is 2.87 mg/(L·h).展开更多
The corrosion behavior of pure aluminum in FeCl3 solution was investigated mainly by in-situ AFM(Atomic Force Microscopy).The results of combined researches of AFM,SEM(Scanning Electron Microscopy)and EDAX(Energy Disp...The corrosion behavior of pure aluminum in FeCl3 solution was investigated mainly by in-situ AFM(Atomic Force Microscopy).The results of combined researches of AFM,SEM(Scanning Electron Microscopy)and EDAX(Energy Dispersive Analysis of X-ray)show that in addition to uniform attack,pitting corrosion takes place also on pure aluminum surface in FeCl3 solution at open-circuit potential,and impurity elements Fe and Cu are found enriched in corrosion product.In-situ AFM was also used to examine the initiation and development of pitting corrosion of pure aluminum induced by potentiodynamic sweep,and the repassivation of an active pit is observed.AFM tip scratching technique was used to produce a physical defect on metal surface,which is traced by in-situ AFM and it is found that the defect is likely to be preferentially attacked and evolve to pitting corrosion.展开更多
基金National Natural Science Foundation of China,Grant/Award Numbers:21972108,U20A20249,U22A20438Changzhou Science and Technology Bureau,Grant/Award Number:CM20223017Innovation and Technology Commission(ITC)of Hong Kong,The Innovation&Technology Fund(ITF)with Project No.ITS/126/21。
文摘Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P2O7 unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs.
文摘Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.
基金the two referees for very helpful comments and suggestions to improve the quality of the paper.This work was partially supported by the Natural Science Foundation of Zhejiang province of China(LY21A010017)the National Natural Science Foundation of China(12071106,12171130).
文摘This paper concerns the sonic-supersonic structures of the transonic crossflow generated by the steady supersonic flow past an infinite cone of arbitrary cross section.Under the conical assumption,the three-dimensional(3-D)steady Euler equations can be projected onto the unit sphere and the state of fluid can be characterized by the polar and azimuthal angles.Given a segment smooth curve as a conical-sonic line in the polar-azimuthal angle plane,we construct a classical conical-supersonic solution near the curve under some reasonable assumptions.To overcome the difficulty caused by the parabolic degeneracy,we apply the characteristic decomposition technique to transform the Euler equations into a new degenerate hyperbolic system in a partial hodograph plane.The singular terms are isolated from the highly nonlinear complicated system and then can be handled successfully.We establish a smooth local solution to the new system in a suitable weighted metric space and then express the solution in terms of the original variables.
基金financially supported by the National Nature Science Foundation of China (No. 51174115)National Outstanding Youth Science Foundation of China (No. 51025416)Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1065)
文摘Abstract A method of Baotou mixed rare earth concen- trate leaching was investigated. According to the principle of complex leaching, the quadratic orthogonal regression experiment was used to investigate effect of six factors. An optimal condition of low energy and environment friendly was determined as follows: HCl acidity is 4 mol.L-1, AlCl3 concentration is 2 mol.L-l, reaction temperature is 85 ℃, reaction time is 90 rain, liquid to solid ratio is 35 ml.g-1, and stirring speed is 100 r.min-1. According to this condition, the leaching ratio of mixed rare earth con- centrate is 76.5 %. The analyses of X-ray diffraction shows that bastnasite disappears, and the main peaks of filter residue is monazite and cheralite after leaching of HCl- AlCl3 solution. The result indicates that REFCO3 of the mixed rare earth concentrate can be dissolved, but REPO4 remains in the leaching residue. This method provides a way to separate and extract rare earth.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11675084 and 11435005)the Fund from the Educational Commission of Zhejiang Province,China(Grant No.Y201737177)+1 种基金Ningbo Natural Science Foundation(Grant No.2015A610159)the K C Wong Magna Fund in Ningbo University
文摘In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11505154,11605156,11775146,and 11975204)the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LQ16A010003 and LY19A050003)+5 种基金the China Scholarship Council(Grant No.201708330479)the Foundation for Doctoral Program of Zhejiang Ocean University(Grant No.Q1511)the Natural Science Foundation(Grant No.DMS-1664561)the Distinguished Professorships by Shanghai University of Electric Power(China)North-West University(South Africa)King Abdulaziz University(Saudi Arabia)
文摘Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.
基金Project supported bythe National Natural Science Foundation of China (50306008) and the Fund fromthe Preli minary Research Project of General Equipment Ministry (41328030507)
文摘Perovskite LaMnO3 powders with an average crystallite size of 12.5 nm were rapidly synthesized via a microwave-induced autocombustion reaction using glycine as a fuel and nitrate as an oxidant. After self-propagating combustion, the desired nanocrystalline perovskite LaMnO3 was obtained and no further calcination was carried out. The possible processes of combustion reaction were discussed according to the principle of propellant chemistry. The autocombustion and thermal decomposition of the precursor were investigated using the TG-DTA and FT-IR techniques. The influences of glycine-nitrate molar ratio and heat-treatment temperature on the perovskite phase formation and crystallite size of as-burnt powder were studied by XRD. The morphology and size of the as-burnt powder before and after milling were characterized and compared by TEM.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10735030,90718041 and 40975038)Shanghai Leading Academic Discipline Project(Grant No.B412)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT0734)
文摘This paper investigates an important high-dimensional model in the atmospheric and oceanic dynamics-(3+1)- dimensional nonlinear baroclinic potential vorticity equation by the classical Lie group method. Its symmetry algebra, symmetry group and group-invariant solutions are analysed. Otherwise, some exact explicit solutions are obtained from the corresponding (2+1)-dimensional equation, the inviscid barotropic nondivergent vorticy equation. To show the properties and characters of these solutions, some plots as well as their possible physical meanings of the atmospheric circulation are given out.
基金supported by the National Natural Science Foundation of China,Nos.41874001 and 41664001Support Program for Outstanding Youth Talents in Jiangxi Province,No.20162BCB23050National Key Research and Development Program,No.2016YFB0501405。
文摘When linearizing three-dimensional(3 D)coordinate similarity transformation model with large rotations,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3 D coordinate similarity transformation model in this paper.We deduced a complete solution for the 3 D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the condition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.
基金Project supported by the Scientific Research Foundation of Lishui University, China (Grant No. KZ201110)
文摘By using the (G'/G)-expansion method and the variable separation method, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is obtained. Based on the derived solitary wave solutions, we obtain some special localized excitations and study the interactions between two solitary waves of the system.
基金Project(15B003)supported by the Outlayed-up Youth Project of Hunan Provincial Department of Education,ChinaProject(KY201623)supported by the Housing and Urban Construction Department of Hunan Province,China+1 种基金Project(2016CL02)supported by the Hunan Provincial Key Laboratory of Materials Protection for Electric Power and Transportation,ChinaProject(11405013)supported by the National Natural Science Foundation of China
文摘Electrospun WO_3 nanofibers were fabricated by coaxial electrospinning and directly annealing WCl_6/polyvinylpyrrolidone(PVP) nanofibers on activated carbon fibres(ACF), and characterized by scanning electron microscopy(SEM) and X-ray diffractometry(XRD). The most suitable condition for electrospinning is the mass ratio of WCl_6 to PVP 0.6, appropriate amount DMF and ethanol, a voltage of 28 kV, the reception distance of 15 cm, the humidity range within 10% and 20% and the moving rate of the pump 0.001 mm/s. The photocatalytic activities of WO_3 nanofibers were evaluated by the photo-degradation of phenol solution under the irradiation of 500 W xenon lamp. The results showed that, the sizes of the fibers are about 100 nm, and after being photodegraded for 210 min, the concentration of phenol decreased from 20.05 mg/L to 8.60 mg/L. Thus, the photo-degradation rate of WO_3 nanofibers for phenol solution is 2.87 mg/(L·h).
文摘The corrosion behavior of pure aluminum in FeCl3 solution was investigated mainly by in-situ AFM(Atomic Force Microscopy).The results of combined researches of AFM,SEM(Scanning Electron Microscopy)and EDAX(Energy Dispersive Analysis of X-ray)show that in addition to uniform attack,pitting corrosion takes place also on pure aluminum surface in FeCl3 solution at open-circuit potential,and impurity elements Fe and Cu are found enriched in corrosion product.In-situ AFM was also used to examine the initiation and development of pitting corrosion of pure aluminum induced by potentiodynamic sweep,and the repassivation of an active pit is observed.AFM tip scratching technique was used to produce a physical defect on metal surface,which is traced by in-situ AFM and it is found that the defect is likely to be preferentially attacked and evolve to pitting corrosion.
基金supported by the National Natural Science Foundation of China(No.50807042)the Research Fund for the Doctoral Program of Higher Education of China(No.200806981043)+1 种基金the Fundamental Research Fund for the Central Universities(No.xjj2012088)the fund of StateKey Laboratory of Electrical Insulation and Power Equipment(Xi'an Jiaotong University No.EIPE12305)