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 P_(2)O_(7) 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
Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generator...Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.展开更多
It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analyt...It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.展开更多
The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions f...The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions for preparing well-dispersed nanoparticles were found as follows: 0.4 mol/L NaBH4 was added into solution containing 0.2 mol/L Cu2+, 1.0% gelatin dispersant in mass fraction, and 1.2 mol/L NH3?H2O at pH 12 and 313 K. In addition, a series of experiments were performed to discover the reaction process. NH3?H2O was found to be able to modulate the reaction process. At pH=10, Cu2+ was transformed to Cu(NH3)42+ as precursor after the addition of NH3?H2O, and then Cu(NH3)42+ was reduced by NaBH4 solution. At pH=12, Cu2+ was transformed to Cu(OH)2 as precursor after the addition of NH3?H2O, and Cu(OH)2 was then reduced by NaBH4 solution.展开更多
Due to the negligible non-perturbation effect in the low-energy region, quantum chromodynamics (QCD) is limited to be applied to hadron problems in particle physics. However, QED has mature non-perturbation models w...Due to the negligible non-perturbation effect in the low-energy region, quantum chromodynamics (QCD) is limited to be applied to hadron problems in particle physics. However, QED has mature non-perturbation models which can be applied to Fermi acting-energy between quark and gluon. This paper applies quantum electrodynamics in 2 + 1 dimensions (QED3) to the Fermi condensation problems. First, the Dyson-Schwinger equation which the fermions satisfy is constructed, and then the Fermi energy gap is solved. Theoretical calculations show that within the chirality limit, there exist three solutions for the energy gap; beyond the chirality limit, there are two solutions; all these solutions correspond to different fermion condensates. It can be concluded that the fermion condensates within the chirality limit can be used to analyze the existence of antiferromagnetic, pseudogap, and superconducting phases, and two fermion condensates are discovered beyond the chirality limit.展开更多
Ni-Y2O3 nanocomposite powder with uniform distribution of fine oxide particles in the metal matrix was successfully fabricated via solution combustion process followed by hydrogen reduction. The combustion behavior wa...Ni-Y2O3 nanocomposite powder with uniform distribution of fine oxide particles in the metal matrix was successfully fabricated via solution combustion process followed by hydrogen reduction. The combustion behavior was investigated by DTA-TG analysis. The influence of urea to nickel nitrate(U/Ni) ratio on the combustion behavior and morphology evolution of the combusted powder was investigated. The morphological characteristics and phase transformation of the combusted powder and the reduced powder were characterized by FESEM, TEM and XRD. The HRTEM image of Ni-Y2O3 nanocomposite powder indicated that Y2O3 particles with average particle size of about 10 nm dispersed uniformly in the nickel matrix.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
We develop a 3D bounded slice-surface grid (3D-BSSG) structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSS...We develop a 3D bounded slice-surface grid (3D-BSSG) structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.展开更多
Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled ...Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.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
This study investigated the removal of hexavalent chromium(Cr(VI)) in aqueous solutions using pomelo peel(PP) and FeCl3-modified pomelo peel(FPP) as novel biomass adsorbents.Batch adsorption experiments were performed...This study investigated the removal of hexavalent chromium(Cr(VI)) in aqueous solutions using pomelo peel(PP) and FeCl3-modified pomelo peel(FPP) as novel biomass adsorbents.Batch adsorption experiments were performed to evaluate the effects of pH,time,temperature,initial concentration,and adsorbent dose on Cr(VI) removal by PP and FPP.The results show that the maximum adsorption capacity of Cr(VI)was 21.55 mg/g for FPP and 0.57 mg/g for PP at a pH of 2.0 and a temperature of 40℃.The surface shape,microstructure,and chemical composition of FPP were analyzed with scanning electron microscopy(SEM),Fourier transform infrared spectroscopy(FTIR),and energy dispersive spectroscopy(EDS),and compared with those of PP.The results show that the adsorption performance of FPP was much better than that of PP,indicating that FPP can be an alternative high-efficiency adsorbent for Cr(VI) removal.展开更多
Using elementary integral method, a complete classification of all possible exact traveling wave solutions to (3+1)-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK's direct method, we build the relationship between new solutions and old ones and the (3+1)-d...Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK's direct method, we build the relationship between new solutions and old ones and the (3+1)-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the (3+1)-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.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
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 P_(2)O_(7) 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Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.
文摘It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.
文摘The preparation of Cu nanoparticles by the aqueous solution reduction method was investigated. The effects of different reaction parameters on the preparation of Cu nanoparticles were studied. The optimum conditions for preparing well-dispersed nanoparticles were found as follows: 0.4 mol/L NaBH4 was added into solution containing 0.2 mol/L Cu2+, 1.0% gelatin dispersant in mass fraction, and 1.2 mol/L NH3?H2O at pH 12 and 313 K. In addition, a series of experiments were performed to discover the reaction process. NH3?H2O was found to be able to modulate the reaction process. At pH=10, Cu2+ was transformed to Cu(NH3)42+ as precursor after the addition of NH3?H2O, and then Cu(NH3)42+ was reduced by NaBH4 solution. At pH=12, Cu2+ was transformed to Cu(OH)2 as precursor after the addition of NH3?H2O, and Cu(OH)2 was then reduced by NaBH4 solution.
基金The National Natural Science Foundation of China(No.11047005)the Science Foundation of Southeast University
文摘Due to the negligible non-perturbation effect in the low-energy region, quantum chromodynamics (QCD) is limited to be applied to hadron problems in particle physics. However, QED has mature non-perturbation models which can be applied to Fermi acting-energy between quark and gluon. This paper applies quantum electrodynamics in 2 + 1 dimensions (QED3) to the Fermi condensation problems. First, the Dyson-Schwinger equation which the fermions satisfy is constructed, and then the Fermi energy gap is solved. Theoretical calculations show that within the chirality limit, there exist three solutions for the energy gap; beyond the chirality limit, there are two solutions; all these solutions correspond to different fermion condensates. It can be concluded that the fermion condensates within the chirality limit can be used to analyze the existence of antiferromagnetic, pseudogap, and superconducting phases, and two fermion condensates are discovered beyond the chirality limit.
基金Project(2132046)supported by the Beijing Natural Science Foundation,ChinaProject(51104007)supported by the National Natural Science Foundation of China
文摘Ni-Y2O3 nanocomposite powder with uniform distribution of fine oxide particles in the metal matrix was successfully fabricated via solution combustion process followed by hydrogen reduction. The combustion behavior was investigated by DTA-TG analysis. The influence of urea to nickel nitrate(U/Ni) ratio on the combustion behavior and morphology evolution of the combusted powder was investigated. The morphological characteristics and phase transformation of the combusted powder and the reduced powder were characterized by FESEM, TEM and XRD. The HRTEM image of Ni-Y2O3 nanocomposite powder indicated that Y2O3 particles with average particle size of about 10 nm dispersed uniformly in the nickel matrix.
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.
文摘We develop a 3D bounded slice-surface grid (3D-BSSG) structure for representation and introduce the solution space smoothing technique to search for the optimal solution. Experiment results demonstrate that a 3D-BSSG structure based algorithm is very effective and efficient.
文摘Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.
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supported by the National Key Research and Development Program of China(Grant No.2018YFD1100504)the Natural Science Foundation of Hunan Province,China(Grant No.2017JJ2277).
文摘This study investigated the removal of hexavalent chromium(Cr(VI)) in aqueous solutions using pomelo peel(PP) and FeCl3-modified pomelo peel(FPP) as novel biomass adsorbents.Batch adsorption experiments were performed to evaluate the effects of pH,time,temperature,initial concentration,and adsorbent dose on Cr(VI) removal by PP and FPP.The results show that the maximum adsorption capacity of Cr(VI)was 21.55 mg/g for FPP and 0.57 mg/g for PP at a pH of 2.0 and a temperature of 40℃.The surface shape,microstructure,and chemical composition of FPP were analyzed with scanning electron microscopy(SEM),Fourier transform infrared spectroscopy(FTIR),and energy dispersive spectroscopy(EDS),and compared with those of PP.The results show that the adsorption performance of FPP was much better than that of PP,indicating that FPP can be an alternative high-efficiency adsorbent for Cr(VI) removal.
基金The project supported by Scientific Research Fund of Heilongjiang Province of China under Grant No. 11511008The author would like to thank referees for their valuable suggestions.
文摘Using elementary integral method, a complete classification of all possible exact traveling wave solutions to (3+1)-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004zx16 tCorresponding author, E-maih zzlh100@163.com
文摘Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK's direct method, we build the relationship between new solutions and old ones and the (3+1)-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the (3+1)-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.
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.