The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The...The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The approach of the π-equation to predict separating results and to control the separating processes is presented with examples.展开更多
Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional the...Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios(10^3 lnb)and103lna of 44 Ca/40 Ca in forsterite(Fo)are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca+Mg)varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/(Ca+Mg)is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 10^3 lnb is negatively correlated with Ca–O bond length,the 10^3lnb significantly increases with decreasing Ca/(Ca+Mg)when 1/64<Ca/(Ca+Mg)<2/16.As a consequence,the 10^3lna between forsterite and other minerals also strongly depend on the Ca content in forsterite.Combining previous studies with our results,the heavier Ca isotopes enrichment sequence in minerals is:forsterite[orthopyroxene[clinopyroxene[calcite & diopside[dolomite[aragonite.Olivineand pyroxenes are enriched in heavier Ca isotope compared to carbonates.The 10^3lna between forsterite with a Ca/(Ca+Mg)of 1/64 and clinopyroxene(Ca/Mg=1/1,i.e.,diopside)is up to^0.64%at 1200 K.The large 103lnaFodiopsiderelative to the current analytical precision for Ca isotope measurements suggests that the dependence of10^3 lnaFo-diopsideon temperature can be used as a thermometer,similar to the one based on the 103lna of 44 Ca/40 Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.展开更多
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdin...In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.展开更多
In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scal...In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.展开更多
In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws...In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.展开更多
Based on the measured activities, the phase diagrams and the annexation principle, the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated. The calculated results agree w...Based on the measured activities, the phase diagrams and the annexation principle, the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated. The calculated results agree with practice and obey the mass action law, showing that the models formulated can reflect the structural characteristics of both melts. Meanwhile, it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts. The melts involving eulectic which give rise to phase separation, and in which activities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.展开更多
Based on the principle of annexation and phase diagrams, the structural units of In Pb Sb and In Bi Pb melts were determined, and their calculating models of mass action concentrations were formulated. Calculated resu...Based on the principle of annexation and phase diagrams, the structural units of In Pb Sb and In Bi Pb melts were determined, and their calculating models of mass action concentrations were formulated. Calculated results agree well with practical values, which in turn show that the models deduced can reflect the structural realities of corresponding melts and the principle of annexation is applicable not only to some binary metallic melts, but also to ternary metallic melts.展开更多
Based on the measured activities,the phase diagrams and the annexation principle,the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated.The calculated results agree with...Based on the measured activities,the phase diagrams and the annexation principle,the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated.The calculated results agree with practice and obey the mass action law,showing that the models formulated can reflect the structural characteristics of both melts.Meanwhile,it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts.The melts involving eutectic which give rise to phase separation,and in which activcities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.展开更多
In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical expo...In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods.展开更多
文摘The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The approach of the π-equation to predict separating results and to control the separating processes is presented with examples.
基金financially supported by the Natural Science Foundation of China (Nos. 41721002, 41473011)Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund
文摘Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios(10^3 lnb)and103lna of 44 Ca/40 Ca in forsterite(Fo)are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca+Mg)varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/(Ca+Mg)is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 10^3 lnb is negatively correlated with Ca–O bond length,the 10^3lnb significantly increases with decreasing Ca/(Ca+Mg)when 1/64<Ca/(Ca+Mg)<2/16.As a consequence,the 10^3lna between forsterite and other minerals also strongly depend on the Ca content in forsterite.Combining previous studies with our results,the heavier Ca isotopes enrichment sequence in minerals is:forsterite[orthopyroxene[clinopyroxene[calcite & diopside[dolomite[aragonite.Olivineand pyroxenes are enriched in heavier Ca isotope compared to carbonates.The 10^3lna between forsterite with a Ca/(Ca+Mg)of 1/64 and clinopyroxene(Ca/Mg=1/1,i.e.,diopside)is up to^0.64%at 1200 K.The large 103lnaFodiopsiderelative to the current analytical precision for Ca isotope measurements suggests that the dependence of10^3 lnaFo-diopsideon temperature can be used as a thermometer,similar to the one based on the 103lna of 44 Ca/40 Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.
基金supported by National Science Foundation of China (11071177)
文摘In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.
基金supported by the National Natural Science Foundation of China(11471236,11561049)
文摘In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle(see Qiu, 2014), we prove a new version of Ekeland variational principle(briefly, denoted by EVP), which is quite different from the previous ones, for the objective function consists of a family of scalar functions. From the new version, we deduce several vectorial EVPs for cyclically antimonotone equilibrium problems, which extend and improve the previous results. By developing the original method proposed by Castellani and Giuli, we deduce a number of existence results(no matter scalar-valued case,or vector-valued case), when the feasible set is a sequentially compact topological space or a countably compact topological space. Finally, we propose a general coercivity condition. Combining the general coercivity condition and the obtained existence results with compactness conditions, we obtain several existence results for equilibrium problems in noncompact settings.
基金Project supported by the National Natural Science Foundation of China(No.11571366)the Basic Research Foundation of National Numerical Wind Tunnel Project(No.NNW2018-ZT4A08)
文摘In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.
文摘Based on the measured activities, the phase diagrams and the annexation principle, the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated. The calculated results agree with practice and obey the mass action law, showing that the models formulated can reflect the structural characteristics of both melts. Meanwhile, it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts. The melts involving eulectic which give rise to phase separation, and in which activities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.
文摘Based on the principle of annexation and phase diagrams, the structural units of In Pb Sb and In Bi Pb melts were determined, and their calculating models of mass action concentrations were formulated. Calculated results agree well with practical values, which in turn show that the models deduced can reflect the structural realities of corresponding melts and the principle of annexation is applicable not only to some binary metallic melts, but also to ternary metallic melts.
文摘Based on the measured activities,the phase diagrams and the annexation principle,the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated.The calculated results agree with practice and obey the mass action law,showing that the models formulated can reflect the structural characteristics of both melts.Meanwhile,it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts.The melts involving eutectic which give rise to phase separation,and in which activcities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.
基金supported by the NNSF of China(12171014, 12271539, 12171326)the Beijing Municipal Commission of Education (KZ202010028048)the Research Foundation for Advanced Talents of Beijing Technology and Business University (19008022326)。
文摘In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods.