The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional Boussinesq equation as a simple example, six types o...The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional Boussinesq equation as a simple example, six types of conditional similarity reductions are obtained.展开更多
Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cann...Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.展开更多
We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the （2＋1）-dimensional modifie...We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the （2＋1）-dimensional modified Broer- Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations.展开更多
The development of a non-precious metal electrocatalyst （NPME） with a performance superior to commercial Pt/C for the oxygen reduction reaction （ORR） is important for the commercialization of fuel cells. We report...The development of a non-precious metal electrocatalyst （NPME） with a performance superior to commercial Pt/C for the oxygen reduction reaction （ORR） is important for the commercialization of fuel cells. We report the synthesis of a NPME by heat-treating Co-based metal organic frameworks （ZIF-67） with a small average size of 44 nm. The electrocatalyst pyrolyzed at 600 ~C showed the best performance and the performance was enhanced when it was supported on BP 2000. The resulting electrocatalyst was composed of 10 nm Co nanoparticles coated by 3-12 layers of N doped graphite layers which as a whole was embedded in a carbon matrix. The ORR performance of the electrocatalyst was tested by rotating disk electrode tests in O2-saturated 0.1 mol/L KOH under ambient conditions. The electrocatalyst （1.0 mg/cm~] showed an onset potential of 1.017 V （[vs. RHE] and a half-wave potential of 0.857 V （vs. RHE], which showed it was as good as the commer- cial Pt/C （20 BgPt/cm2）. Furthermore, the electrocatalyst possessed much better stability and re- sistance to methanol crossover than Pt/C.展开更多
Embedding direct reduction followed by magnetic separation was conducted to fully recover iron and titanium separately from beach titanomagnetite （TTM）. The influences of reduction conditions, such as molar ratio of...Embedding direct reduction followed by magnetic separation was conducted to fully recover iron and titanium separately from beach titanomagnetite （TTM）. The influences of reduction conditions, such as molar ratio of C to Fe, reduction time, and reduction temperature, were studied. The results showed that the TTM concentrate was reduced to iron and iron-titanium oxides, depending on the reduction time, and the reduction sequence at 1 200℃ was suggested as follows ： Fe2.75 Ti0.25O4→Fe2TiO4→FeTiO3→FeTi2O5. The reduction temperature played a considerable role in the reduction of TTM concentrates. Increasing temperature from 1 100 to 1 200℃ was beneficial to recovering titanium and iron, whereas the results deteriorated as temperature increased further. The results of X-ray diffraction and scanning electron microscopy analyses showed that low temperature （≤1100℃） was unfavorable for the gasification of reductant, resulting in insufficient reducing atmosphere in the reduction process. The molten phase was formed at high temperatures of 1250-1 300℃, which accelerated the migration rate of metallic particles and suppressed the diffusion of reduction gas, resulting in poor reduction. The optimum conditions for reducing TTM concentrate are as follows： molar ratio of C to Fe of 1.68, reduction time of 150 min, and reduction temperature of 1 200℃. Under these conditions, direct reduction iron powder, assaying 90.28 mass% TFe and 1.73 mass% TiO2 with iron recovery of 90.85%, and titanium concentrate, assaying 46.24 mass% TiO2 with TiO2 recovery of 91.15%, were obtained.展开更多
With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we invest...With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.展开更多
The purpose of this study was to investigate the effect of preadsorbed CO at different temperatures, calcination temperatures, the combined influence of reduction temperature and time, and pretreatment using hydrogen ...The purpose of this study was to investigate the effect of preadsorbed CO at different temperatures, calcination temperatures, the combined influence of reduction temperature and time, and pretreatment using hydrogen or syngas as reduction agents on the F-T synthesis （FTS） activity and selectivity of Co/Al2O3 catalyst. The reactivity of the carbon species at higher preadsorption temperature with H2 in TPSR decreased, whereas the carbon-containing species showed higher reactivity over Co/Al2O3 catalyst with low calcination temperature. This agreed well with the order of catalytic activity for F-T synthesis on this catalyst. The catalytic activity of the catalyst varied with reduction temperature and time remarkably. CODEX optimization gave an optimum reduction temperature of 756 K and reduction time of 6.2 h and estimated C5＋ yield perfectly. The pretreatment of Co/Al2O3 catalyst with different reduction agents （hydrogen or syngas） showed important influences on the catalytic performance. A high CO conversion and C5＋ yield were obtained on the catalyst reduced by hydrogen, whereas methane selectivity on the catalyst reduced by syngas was much higher than that on the catalyst reduced by hydrogen.展开更多
It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potential...It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem, and then shows that the restricted KdV flows, such as the Neumann system, the Gamier system and the generalized multicomponent Henon-Hieles system, are a kind of special reductions of the restricted AKNS flows.展开更多
文摘The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional Boussinesq equation as a simple example, six types of conditional similarity reductions are obtained.
基金国家杰出青年科学基金，the Research Fund for the Doctoral Program of Higher Education of China
文摘Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272071 and the Natural Science Foundation of Zhejiang Province of China under Grant No. Y606049
文摘We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the （2＋1）-dimensional modified Broer- Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations.
基金supported by the National Basic Research Program of China(973 Program,2015CB932304)the National Natural Science Founda-tion of China(21436003)
文摘The development of a non-precious metal electrocatalyst （NPME） with a performance superior to commercial Pt/C for the oxygen reduction reaction （ORR） is important for the commercialization of fuel cells. We report the synthesis of a NPME by heat-treating Co-based metal organic frameworks （ZIF-67） with a small average size of 44 nm. The electrocatalyst pyrolyzed at 600 ~C showed the best performance and the performance was enhanced when it was supported on BP 2000. The resulting electrocatalyst was composed of 10 nm Co nanoparticles coated by 3-12 layers of N doped graphite layers which as a whole was embedded in a carbon matrix. The ORR performance of the electrocatalyst was tested by rotating disk electrode tests in O2-saturated 0.1 mol/L KOH under ambient conditions. The electrocatalyst （1.0 mg/cm~] showed an onset potential of 1.017 V （[vs. RHE] and a half-wave potential of 0.857 V （vs. RHE], which showed it was as good as the commer- cial Pt/C （20 BgPt/cm2）. Furthermore, the electrocatalyst possessed much better stability and re- sistance to methanol crossover than Pt/C.
基金financially supported by the National Natural Science Foundation of China (Grant No.51474018)
文摘Embedding direct reduction followed by magnetic separation was conducted to fully recover iron and titanium separately from beach titanomagnetite （TTM）. The influences of reduction conditions, such as molar ratio of C to Fe, reduction time, and reduction temperature, were studied. The results showed that the TTM concentrate was reduced to iron and iron-titanium oxides, depending on the reduction time, and the reduction sequence at 1 200℃ was suggested as follows ： Fe2.75 Ti0.25O4→Fe2TiO4→FeTiO3→FeTi2O5. The reduction temperature played a considerable role in the reduction of TTM concentrates. Increasing temperature from 1 100 to 1 200℃ was beneficial to recovering titanium and iron, whereas the results deteriorated as temperature increased further. The results of X-ray diffraction and scanning electron microscopy analyses showed that low temperature （≤1100℃） was unfavorable for the gasification of reductant, resulting in insufficient reducing atmosphere in the reduction process. The molten phase was formed at high temperatures of 1250-1 300℃, which accelerated the migration rate of metallic particles and suppressed the diffusion of reduction gas, resulting in poor reduction. The optimum conditions for reducing TTM concentrate are as follows： molar ratio of C to Fe of 1.68, reduction time of 150 min, and reduction temperature of 1 200℃. Under these conditions, direct reduction iron powder, assaying 90.28 mass% TFe and 1.73 mass% TiO2 with iron recovery of 90.85%, and titanium concentrate, assaying 46.24 mass% TiO2 with TiO2 recovery of 91.15%, were obtained.
基金the Natural Science Foundation of Zhejiang Province under Grant No.Y606128the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ08001the Scientific Research Fund of the Education Department of Zhejiang Province under Grant No.20070568
文摘With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.
基金The National Basic Research Program of China (973 Program) (No. 2005CB221402)China National Petroleum Corporation
文摘The purpose of this study was to investigate the effect of preadsorbed CO at different temperatures, calcination temperatures, the combined influence of reduction temperature and time, and pretreatment using hydrogen or syngas as reduction agents on the F-T synthesis （FTS） activity and selectivity of Co/Al2O3 catalyst. The reactivity of the carbon species at higher preadsorption temperature with H2 in TPSR decreased, whereas the carbon-containing species showed higher reactivity over Co/Al2O3 catalyst with low calcination temperature. This agreed well with the order of catalytic activity for F-T synthesis on this catalyst. The catalytic activity of the catalyst varied with reduction temperature and time remarkably. CODEX optimization gave an optimum reduction temperature of 756 K and reduction time of 6.2 h and estimated C5＋ yield perfectly. The pretreatment of Co/Al2O3 catalyst with different reduction agents （hydrogen or syngas） showed important influences on the catalytic performance. A high CO conversion and C5＋ yield were obtained on the catalyst reduced by hydrogen, whereas methane selectivity on the catalyst reduced by syngas was much higher than that on the catalyst reduced by hydrogen.
基金Project supported by the National Natural Science Foundation of China (No.10871165)
文摘It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem, and then shows that the restricted KdV flows, such as the Neumann system, the Gamier system and the generalized multicomponent Henon-Hieles system, are a kind of special reductions of the restricted AKNS flows.
