We expand the step-transition operator of any linear multi-step method with order s≥ 2 up to O(Ts+5). And through examples we show how much the perturbation of the step-transition operator caused by the error of init...We expand the step-transition operator of any linear multi-step method with order s≥ 2 up to O(Ts+5). And through examples we show how much the perturbation of the step-transition operator caused by the error of initial value is.展开更多
We prove that any linear multi-step method G1^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH（Zk） with odd order u （u≥ 3） cannot be conjugate to a symplectic method G2^T of order w （w 〉 u） via any generalize...We prove that any linear multi-step method G1^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH（Zk） with odd order u （u≥ 3） cannot be conjugate to a symplectic method G2^T of order w （w 〉 u） via any generalized linear multi-step method G3^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH（∑l=0^mγklZl）. We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when G3^T is a more general operator.展开更多
The present study deals with the study of the velocity distribution and the separation phenomenon of flow of air over a two dimensional backward facing step. The flow of air over a backward facing step has been invest...The present study deals with the study of the velocity distribution and the separation phenomenon of flow of air over a two dimensional backward facing step. The flow of air over a backward facing step has been investigated numerically using FLUENT. Flow simulation has been carried out in a backward facing step having an expansion ratio （ratio of the height before and after the step） of 1：1.94 and the results obtained are compared with the published experimental results. Comparison of flow characteristics between steps with three different transitions is made. The variation ofreattachment length for all the three cases are analyzed for wide range of Reynolds number ranging from 100 to 7000 which covers the laminar, transition and turbulent flow of air. Simulation of the flow over steps with expansion ratios of 1：1.24, 1：1.38, 1：1.47, 1：1.53, 1：1.94, 1：2.20 are also carried out to examine the effect of different expansion ratios on the reattachment length. It is found that the primary reattachment length increases with increase in the expansion ratio. The primary reattachment length at the bottom wall downstream of the step is minimum for the step with round edged transition and maximum for the step with a vertical drop transition.展开更多
Comprehensive Summary,Regulating spin crossover(SCO)behavior,especially controlling the spin transition steps,is an important scientific issue,mainly because people aim to control spin bistability and multistability.P...Comprehensive Summary,Regulating spin crossover(SCO)behavior,especially controlling the spin transition steps,is an important scientific issue,mainly because people aim to control spin bistability and multistability.Presently,SCO bistability can be regulated by changing the ligand-modifying species,non-coordinated anions,guest molecules,and metal-ion dopant.However,the control of multistability is extremely challenging,especially in Fe(III)SCO compounds.Here,we report that[FeIII(H-5-Br-thsa)(5-Br-thsa)]·H2O(5-Br-thsa=(5-bromo-2-hydroxybenzylidene)hydrazinecarbothioamide),a compound we have reported before,exists in two polymorphic forms:polymorph 1 exhibits three-step SCO,and polymorph 2 shows five-step SCO,with multi-step SCO behavior effectively regulated by polymorphism.According to single-crystal and powder X-ray diffractometry,polymorphs 1 and 2 crystallize in different space groups during their spin transitions,with two-step symmetry breaking observed(Pbcn→Pnc2→Pbcn for polymorph 1;P21/n→Pn→P21/n for polymorph 2).We realized that the behavior of these two polymorphs depends significantly on the structure,including(i)the average Fe—N bond distance,(ii)deformation of octahedral FeIII atoms,and(iii)distinct crystal packing,which account for the large differences observed in magnetic properties.展开更多
Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained...Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.展开更多
Wagner problem is originally concerned with inviscid flow and unsteady force due to a small step motion,or attaining of a small angle of attack,of an airfoil in an initially uniform flow and has been studied recently ...Wagner problem is originally concerned with inviscid flow and unsteady force due to a small step motion,or attaining of a small angle of attack,of an airfoil in an initially uniform flow and has been studied recently for inviscid flow with large amplitude step motion.Here we propose to consider turbulent Wagner problem for a plate that is initially covered with a mixed laminarboundary layer on both sides and is set into step motion of small or large amplitude and in direction normal to the plate.The evolution of skin friction and transition region in time are examined numerically.It is found that transition region unexpectedly changes direction of movement for small amplitude of step motion while global transition or laminarization exists for large amplitude step motion.The significance of this study is twofold.First,the present study treated a new and interesting problem since it combines two problems of fundamental interests,one is Wagner problem and the other is boundary layer transition.Second,the present study appears to show that the pressure gradient normal to the airfoil and caused by discontinuous step motion may have subtle influence on transition and the mechanism of this influence deserves further studies.展开更多
Developing large scale deposition techniques to fabricate thin porous films with suitable opto-electro nic properties for water catalysis is a necessity to mitigate climate change and have a sustainable environment.In...Developing large scale deposition techniques to fabricate thin porous films with suitable opto-electro nic properties for water catalysis is a necessity to mitigate climate change and have a sustainable environment.In this review,flame spray pyrolysis(FSP)technique,a rapid and scalable methodology to synthesize nanostructured transitional metal oxide films with designed functionalities,is firstly introduced.Furthermore,applications in electrochemical(EC)and photoelectrochemical(PEC)water splitting for the production of hydrogen fuel is also presented.The high combustion temperature and the aggregation of flame aerosol ensure that the FSP-made films possess high crystallinity,tunable porosity and high surface areas,making this method suitable either as catalysts for EC water splitting or as efficient semiconductor materials for PEC water splitting.Finally,a perspective on the next generation FSP engineered films with potential applications in energy storage and conversion is described.展开更多
We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate...We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate operator of STO of any DS.展开更多
在高增益场合,传统Boost变换器存在增益受限、器件应力大、效率低等问题,为此,提出一种交错控制高增益零电流转移(zero current transition,ZCT)ZCT Boost变换器,详细分析其工作原理,在此基础上对其电压增益进行推导,讨论其软开关工作条...在高增益场合,传统Boost变换器存在增益受限、器件应力大、效率低等问题,为此,提出一种交错控制高增益零电流转移(zero current transition,ZCT)ZCT Boost变换器,详细分析其工作原理,在此基础上对其电压增益进行推导,讨论其软开关工作条件,特别分析考虑二极管反向恢复时变换器的工作情况。最后搭建一台额定输入电压为12 V、输出电压为100 V、输出功率为35 W的实验样机,变换效率最高达到87.7%,实验结果验证了理论分析的正确性。展开更多
基金Special Funds for Major State Basic Research Projects of China (No.G1999032801-10 and No. G1999032804), by the knowledge inn
文摘We expand the step-transition operator of any linear multi-step method with order s≥ 2 up to O(Ts+5). And through examples we show how much the perturbation of the step-transition operator caused by the error of initial value is.
基金Acknowledgements. We would like to thank the editors for their valuable suggestions and corrections. This research is supported by the National Natural Science Foundation of China （Grant Nos. 10471145 and 10672143）, and by Morningside Center of Mathematics, Chinese Academy of Sciences.
文摘We prove that any linear multi-step method G1^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH（Zk） with odd order u （u≥ 3） cannot be conjugate to a symplectic method G2^T of order w （w 〉 u） via any generalized linear multi-step method G3^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH（∑l=0^mγklZl）. We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when G3^T is a more general operator.
文摘The present study deals with the study of the velocity distribution and the separation phenomenon of flow of air over a two dimensional backward facing step. The flow of air over a backward facing step has been investigated numerically using FLUENT. Flow simulation has been carried out in a backward facing step having an expansion ratio （ratio of the height before and after the step） of 1：1.94 and the results obtained are compared with the published experimental results. Comparison of flow characteristics between steps with three different transitions is made. The variation ofreattachment length for all the three cases are analyzed for wide range of Reynolds number ranging from 100 to 7000 which covers the laminar, transition and turbulent flow of air. Simulation of the flow over steps with expansion ratios of 1：1.24, 1：1.38, 1：1.47, 1：1.53, 1：1.94, 1：2.20 are also carried out to examine the effect of different expansion ratios on the reattachment length. It is found that the primary reattachment length increases with increase in the expansion ratio. The primary reattachment length at the bottom wall downstream of the step is minimum for the step with round edged transition and maximum for the step with a vertical drop transition.
基金supported by the National Natural Science Foundation of China(NSFC,21971124,22275100,22150710513)the Ph.D.Candidate Research Innovation Fund of the NkU School of Materials Science and Engineering.
文摘Comprehensive Summary,Regulating spin crossover(SCO)behavior,especially controlling the spin transition steps,is an important scientific issue,mainly because people aim to control spin bistability and multistability.Presently,SCO bistability can be regulated by changing the ligand-modifying species,non-coordinated anions,guest molecules,and metal-ion dopant.However,the control of multistability is extremely challenging,especially in Fe(III)SCO compounds.Here,we report that[FeIII(H-5-Br-thsa)(5-Br-thsa)]·H2O(5-Br-thsa=(5-bromo-2-hydroxybenzylidene)hydrazinecarbothioamide),a compound we have reported before,exists in two polymorphic forms:polymorph 1 exhibits three-step SCO,and polymorph 2 shows five-step SCO,with multi-step SCO behavior effectively regulated by polymorphism.According to single-crystal and powder X-ray diffractometry,polymorphs 1 and 2 crystallize in different space groups during their spin transitions,with two-step symmetry breaking observed(Pbcn→Pnc2→Pbcn for polymorph 1;P21/n→Pn→P21/n for polymorph 2).We realized that the behavior of these two polymorphs depends significantly on the structure,including(i)the average Fe—N bond distance,(ii)deformation of octahedral FeIII atoms,and(iii)distinct crystal packing,which account for the large differences observed in magnetic properties.
基金This research is supported by the Informatization Construction of Knowledge Innovation Projects of the Chinese Academy of Sciences ＂Supercomputing Environment Construction and Application＂ （INF105-SCE）, and by a grant （No. 10471145） from National Natural Science Foundation of China.
文摘Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.
基金supported by the Special Foundation of Chinese Postdoctoral Science(No.2019T120082)Chinese Post-doc Science Foundation(No.2018M640119)the Natural National Science Foundation of China(No.11802157).
文摘Wagner problem is originally concerned with inviscid flow and unsteady force due to a small step motion,or attaining of a small angle of attack,of an airfoil in an initially uniform flow and has been studied recently for inviscid flow with large amplitude step motion.Here we propose to consider turbulent Wagner problem for a plate that is initially covered with a mixed laminarboundary layer on both sides and is set into step motion of small or large amplitude and in direction normal to the plate.The evolution of skin friction and transition region in time are examined numerically.It is found that transition region unexpectedly changes direction of movement for small amplitude of step motion while global transition or laminarization exists for large amplitude step motion.The significance of this study is twofold.First,the present study treated a new and interesting problem since it combines two problems of fundamental interests,one is Wagner problem and the other is boundary layer transition.Second,the present study appears to show that the pressure gradient normal to the airfoil and caused by discontinuous step motion may have subtle influence on transition and the mechanism of this influence deserves further studies.
基金the support of Australian Research Council(ARC)DP150101939,ARC DE160100569Westpac 2016 Research Fellowshipthe ActewAGL Endowment Fund。
文摘Developing large scale deposition techniques to fabricate thin porous films with suitable opto-electro nic properties for water catalysis is a necessity to mitigate climate change and have a sustainable environment.In this review,flame spray pyrolysis(FSP)technique,a rapid and scalable methodology to synthesize nanostructured transitional metal oxide films with designed functionalities,is firstly introduced.Furthermore,applications in electrochemical(EC)and photoelectrochemical(PEC)water splitting for the production of hydrogen fuel is also presented.The high combustion temperature and the aggregation of flame aerosol ensure that the FSP-made films possess high crystallinity,tunable porosity and high surface areas,making this method suitable either as catalysts for EC water splitting or as efficient semiconductor materials for PEC water splitting.Finally,a perspective on the next generation FSP engineered films with potential applications in energy storage and conversion is described.
基金This research is supported by Special Funds for Major State Basic Research Projects of China (No. G1999032801-10 and No. G1999032804) by the knowledge innovation program of the Chinese Academy of Sciences and a grant (No. 19801034) from National Natura
文摘We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate operator of STO of any DS.
