The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution ...The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.展开更多
Graphene-based frameworks suffer from a low quantum capacitance due to graphene’s Dirac point at the Fermi level.This theoretical study investigated the effect structural defects,nitrogen and boron doping,and surface...Graphene-based frameworks suffer from a low quantum capacitance due to graphene’s Dirac point at the Fermi level.This theoretical study investigated the effect structural defects,nitrogen and boron doping,and surface epoxy/hydroxy groups have on the electronic structure and capacitance of graphene.Density functional theory calculations reveal that the lowest energy configurations for nitrogen or boron substitutional doping occur when the dopant atoms are segregated.This elucidates why the magnetic transition for nitrogen doping is experimentally only observed at higher doping levels.We also highlight that the lowest energy configuration for a single vacancy defect is magnetic.Joint density functional theory calculations show that the fixed band approximation becomes increasingly inaccurate for electrolytes with lower dielectric constants.The introduction of structural defects rather than nitrogen or boron substitutional doping,or the introduction of adatoms leads to the largest increase in density of states and capacitance around graphene’s Dirac point.However,the presence of adatoms or substitutional doping leads to a larger shift of the potential of zero charge away from graphene’s Dirac point.展开更多
基金the National Natural Science Foundation of Chinafor Innovative Research Groups Under Grant No.50621062the National Natural Science Foundation of China forYoung Scholars Under Grant No.10402030
文摘The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.
基金supported partially by JST SICORP(Grant No.JPMJSC2112)JST Adaptable and Seamless Technology Transfer Program through Target-driven R&D(A-STEP)(Grant No.JPMJTR22T6),and JSPS KAKENHI(Grant No.22K14757)+1 种基金Calculations were performed using the U.K.National Supercomputing Facility ARCHER2(http://www.archer2.ac.uk)via our membership of the U.K.’s HEC Materials Chemistry Consortium,which is funded by the EPSRC(Grant Nos.EP/L000202 and EP/R029431)the Molecular Modelling Hub for computational resources,MMM Hub,which is partially funded by EPSRC(Grant No.EP/P020194/1).This research has also utilized Queen Mary’s Apocrita HPC facility,supported by QMUL Research-IT.
文摘Graphene-based frameworks suffer from a low quantum capacitance due to graphene’s Dirac point at the Fermi level.This theoretical study investigated the effect structural defects,nitrogen and boron doping,and surface epoxy/hydroxy groups have on the electronic structure and capacitance of graphene.Density functional theory calculations reveal that the lowest energy configurations for nitrogen or boron substitutional doping occur when the dopant atoms are segregated.This elucidates why the magnetic transition for nitrogen doping is experimentally only observed at higher doping levels.We also highlight that the lowest energy configuration for a single vacancy defect is magnetic.Joint density functional theory calculations show that the fixed band approximation becomes increasingly inaccurate for electrolytes with lower dielectric constants.The introduction of structural defects rather than nitrogen or boron substitutional doping,or the introduction of adatoms leads to the largest increase in density of states and capacitance around graphene’s Dirac point.However,the presence of adatoms or substitutional doping leads to a larger shift of the potential of zero charge away from graphene’s Dirac point.
