For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy princi...For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.展开更多
The most recognized and employed model of the solvation equilibration in the ionic solutions was proposed by Eigen and Tamm, in which there are four major states for an ion pair in the solution： the completely solvat...The most recognized and employed model of the solvation equilibration in the ionic solutions was proposed by Eigen and Tamm, in which there are four major states for an ion pair in the solution： the completely solvated state, 2SIP （double solvent separate ion pair）, SIP （single solvent separate ion pair）, and CIP （contact ion pair）. Eigen and Tamm suggested that the transition from SIP to CIP is always the slowest step during the whole pairing process, due to a high free energy barrier between these two states. We carried out a series of potential of mean force calculations to study the pairing free energy profiles of two sets of model mono- atomic 1：1 ion pairs 2.0：x and x：2.0. For 2.0：x pairs the free energy barrier between the SIP and CIP states is largely reduced due to the salvation shell water structure. For these pairs the SIP to CIP transition is thus not the slowest step in the ion pair formation course. This is a deviation from the Eigen-Tamm model.展开更多
Intrinsic carrier transport properties of single-walled carbon nanotubes have been probed by two parallel methods on the same individual tubes： The contactless dielectric force microscopy （DFM） technique and the co...Intrinsic carrier transport properties of single-walled carbon nanotubes have been probed by two parallel methods on the same individual tubes： The contactless dielectric force microscopy （DFM） technique and the conventional field-effect transistor （FET） method. The dielectric responses of SWNTs are strongly correlated with electronic transport of the corresponding FETs. The DC bias voltage in DFM plays a role analogous to the gate voltage in FET. A microscopic model based on the general continuity equation and numerical simulation is built to reveal the link between intrinsic properties such as carrier concentration and mobility and the macroscopic observable, i.e. dielectric responses, in DFM experiments. Local transport barriers in nanotubes, which influence the device transport behaviors, are also detected with nanometer scale resolution.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No. 10962004the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No. 20080404MS0104the Research Foundation for Talented Scholars of Inner Mongolia University under Grant No. 207066
文摘For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.
文摘The most recognized and employed model of the solvation equilibration in the ionic solutions was proposed by Eigen and Tamm, in which there are four major states for an ion pair in the solution： the completely solvated state, 2SIP （double solvent separate ion pair）, SIP （single solvent separate ion pair）, and CIP （contact ion pair）. Eigen and Tamm suggested that the transition from SIP to CIP is always the slowest step during the whole pairing process, due to a high free energy barrier between these two states. We carried out a series of potential of mean force calculations to study the pairing free energy profiles of two sets of model mono- atomic 1：1 ion pairs 2.0：x and x：2.0. For 2.0：x pairs the free energy barrier between the SIP and CIP states is largely reduced due to the salvation shell water structure. For these pairs the SIP to CIP transition is thus not the slowest step in the ion pair formation course. This is a deviation from the Eigen-Tamm model.
文摘Intrinsic carrier transport properties of single-walled carbon nanotubes have been probed by two parallel methods on the same individual tubes： The contactless dielectric force microscopy （DFM） technique and the conventional field-effect transistor （FET） method. The dielectric responses of SWNTs are strongly correlated with electronic transport of the corresponding FETs. The DC bias voltage in DFM plays a role analogous to the gate voltage in FET. A microscopic model based on the general continuity equation and numerical simulation is built to reveal the link between intrinsic properties such as carrier concentration and mobility and the macroscopic observable, i.e. dielectric responses, in DFM experiments. Local transport barriers in nanotubes, which influence the device transport behaviors, are also detected with nanometer scale resolution.
