Critical condition for the transformation from Taylor cone to cone-jet

An energy method is proposed to investigate the critical transformation condition from a Taylor cone to a cone-jet.Based on the kinetic theorem, the system power allocation and the electrohydrodynamics stability are discussed. The numerical results indicate that the energy of the liquid cone tip experiences a maximum value during the transformation.With the proposed jetting energy, we give the critical transformation condition under which the derivative of jetting energy with respect to the surface area is greater than or equal to the energy required to form a unit of new liquid surface.     

两个基于π-共轭二羧酸构筑的配位聚合物的晶体结构、磁性及光催化性能

在水热条件下,利用具有π共轭体系的二羧酸H2L与金属盐进行配位反应得到2个新颖的配位聚合物:{[Mn_2(L)_2(H_2O)_5]·2H_2O}n(1)和[Cd(L)(H_2O)_2]n(2),并通过元素分析、红外光谱、粉末X射线衍射分析、单晶X射线衍射等对其结构进行了表征。结构分析表明,配合物1是具有一维{Mn3(COO)_2}链的二维层状结构,而配合物2中镉离子与L2-配体中的羧基氧螯合配位,最终得到一维链状结构。配合物1和2都通过结构单元之间的氢键作用,最终形成三维超分子结构。此外,还研究了配合物1的磁性和配合物2的光催化活性。     

Poincaré Map Based on Splitting Methods

Firstly, by using the Liouville formula, we prove that the Jacobian matrix determinants of splitting methods are equal to that of the exact flow. However, for the explicit Runge-Kutta methods, there is an error term of order p ＋ I for the Jacobian matrix determinants. Then, the volume evolution law of a given region in phase space is discussed for different algorithms. It is proved that splitting methods can exactly preserve the sum of Lyapunov exponents invariable. Finally, a Poincaré map and its energy distribution of the Duffing equation are computed by using the second-order splitting method and the Heun method （a second-order Runge-Kutta method）. Computation illustrates that the results by splitting methods can properly represent systems＇ chaotic phenomena.     

Structure-Preserving Algorithms for the Lorenz System

Based on a splitting method and a composition method, we construct some structure-preserving algorithms with first-order, second-order and fourth-order accuracy for a Lorenz system. By using the Liouville＇s formula, it is proven that the structure-preserving algorithms exactly preserve the volume of infinitesimal cube for the Lorenz system. Numerical experimental results illustrate that for the conservative Lorenz system, the qualitative behaviour of the trajectories described by the classical explicit fourth-order Runge-Kutta （RK4） method and the fifth-order Runge-Kutta-Fehlberg （RKF45） method is wrong, while the qualitative behaviour derived from the structure-preserving algorithms with different orders of accuracy is correct. Moreover, for the small dissipative Lorenz system, the norm errors of the structure-preserving algorithms in phase space axe less than those of the Runge-Kutta methods.