In order to evaluate the reliability and applicability of the Empirical Orthogonal Functions（EOFs）in the acoustic inversion of sound speed profile（SSP）and reduce EOF＇s dependence on the sample data,a methodology ...In order to evaluate the reliability and applicability of the Empirical Orthogonal Functions（EOFs）in the acoustic inversion of sound speed profile（SSP）and reduce EOF＇s dependence on the sample data,a methodology is proposed for the achievement of the basis functions for SSP＇s expansion.By analyzing the oceanographic dynamics which is the main cause of the SSP＇s variation,the basis functions are obtained naming the Hydrodynamic Normal Modes（HNMs）.The HNM basis functions are almost the same as those derived from the EOF method,while HNMs has less dependence on the amount of the sample data.HNMs method has a physically meaningful interpretation,and it could give out the physical parameters which determine the basis functions for the expansion of SSP,and this makes it possible to analyze and evaluate the trustiness and applicability of EOFs.展开更多
We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis fun...We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.展开更多
基金supported by the National Natural Science Foundation of China(11004214,11274338)the National Defense Foundation of China(9140A03050312ZK0201)
文摘In order to evaluate the reliability and applicability of the Empirical Orthogonal Functions（EOFs）in the acoustic inversion of sound speed profile（SSP）and reduce EOF＇s dependence on the sample data,a methodology is proposed for the achievement of the basis functions for SSP＇s expansion.By analyzing the oceanographic dynamics which is the main cause of the SSP＇s variation,the basis functions are obtained naming the Hydrodynamic Normal Modes（HNMs）.The HNM basis functions are almost the same as those derived from the EOF method,while HNMs has less dependence on the amount of the sample data.HNMs method has a physically meaningful interpretation,and it could give out the physical parameters which determine the basis functions for the expansion of SSP,and this makes it possible to analyze and evaluate the trustiness and applicability of EOFs.
基金supported by the National Natural Science Foundation of China(Grant No.11304169)the Natural Science Foundation of Ningbo City,China(Grant No.2012A610178)+1 种基金the Open Foundation of the Most Important Subjects of Zhejiang Province,China(Grant No.xkzwl1505)K.C.Wong Magna Fund in Ningbo University of China
文摘We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air–water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.
