Nanosystems play an important role in many applications.Due to their complexity,it is challenging to accurately characterize their structure and properties.An important means to reach such a goal is computational simu...Nanosystems play an important role in many applications.Due to their complexity,it is challenging to accurately characterize their structure and properties.An important means to reach such a goal is computational simulation,which is grounded on ab initio electronic structure calculations.Low scaling and accurate electronic-structure algorithms have been developed in recent years.Especially,the efficiency of hybrid density functional calculations for periodic systems has been significantly improved.With electronic structure information,simulation methods can be developed to directly obtain experimentally comparable data.For example,scanning tunneling microscopy images can be effectively simulated with advanced algorithms.When the system we are interested in is strongly coupled to environment,such as the Kondo effect,solving the hierarchical equations of motion turns out to be an effective way of computational characterization.Furthermore,the first principles simulation on the excited state dynamics rapidly emerges in recent years,and nonadiabatic molecular dynamics method plays an important role.For nanosystem involved chemical processes,such as graphene growth,multiscale simulation methods should be developed to characterize their atomic details.In this review,we review some recent progresses in methodology development for computational characterization of nanosystems.Advanced algorithms and software are essential for us to better understand of the nanoworld.展开更多
Since reform and opening up were launched in 1978, China＇s civil law has made progress in terms of both values and systems. Specifically, the status of the individual as the subject of private law has been gradually ...Since reform and opening up were launched in 1978, China＇s civil law has made progress in terms of both values and systems. Specifically, the status of the individual as the subject of private law has been gradually established, the autonomy of private law as the cornerstone of civil law has been laid down, private interests and rights have been recognized and genuinely guaranteed, and the scientific nature of civil law has developed rapidly. However, there is still some room for improvement in degree of formal rationality of current civil law. Upholding the autonomy and formal and rational development of civil law is of great significance for Chinese society. At the same time, it is necessary to preserve a certain degree of openness in civil law in order to overcome some inherent defects in formal rational law.展开更多
We introduce several KAM theorems for infinite-dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori.Especially,we introduce a KAM theorem by Y...We introduce several KAM theorems for infinite-dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori.Especially,we introduce a KAM theorem by Yuan published in CMP(2002),which shows that there are rich KAM tori for a class of Hamiltonian with short range and with linearized operator of pure point spectra.We also present several open problems.展开更多
基金supported by the Ministry of Science and Technology(No.2016YFA0200604)。
文摘Nanosystems play an important role in many applications.Due to their complexity,it is challenging to accurately characterize their structure and properties.An important means to reach such a goal is computational simulation,which is grounded on ab initio electronic structure calculations.Low scaling and accurate electronic-structure algorithms have been developed in recent years.Especially,the efficiency of hybrid density functional calculations for periodic systems has been significantly improved.With electronic structure information,simulation methods can be developed to directly obtain experimentally comparable data.For example,scanning tunneling microscopy images can be effectively simulated with advanced algorithms.When the system we are interested in is strongly coupled to environment,such as the Kondo effect,solving the hierarchical equations of motion turns out to be an effective way of computational characterization.Furthermore,the first principles simulation on the excited state dynamics rapidly emerges in recent years,and nonadiabatic molecular dynamics method plays an important role.For nanosystem involved chemical processes,such as graphene growth,multiscale simulation methods should be developed to characterize their atomic details.In this review,we review some recent progresses in methodology development for computational characterization of nanosystems.Advanced algorithms and software are essential for us to better understand of the nanoworld.
文摘Since reform and opening up were launched in 1978, China＇s civil law has made progress in terms of both values and systems. Specifically, the status of the individual as the subject of private law has been gradually established, the autonomy of private law as the cornerstone of civil law has been laid down, private interests and rights have been recognized and genuinely guaranteed, and the scientific nature of civil law has developed rapidly. However, there is still some room for improvement in degree of formal rationality of current civil law. Upholding the autonomy and formal and rational development of civil law is of great significance for Chinese society. At the same time, it is necessary to preserve a certain degree of openness in civil law in order to overcome some inherent defects in formal rational law.
基金supported by National Natural Science Foundation of China (Grant Nos.11271076 and 11121101)the National Basic Research Program of China (973 Program) (Grant No.2010CB327900)
文摘We introduce several KAM theorems for infinite-dimensional Hamiltonian with short range and discuss the relationship between spectra of linearized operator and invariant tori.Especially,we introduce a KAM theorem by Yuan published in CMP(2002),which shows that there are rich KAM tori for a class of Hamiltonian with short range and with linearized operator of pure point spectra.We also present several open problems.
