In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)...In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)equation.In which,the first order linear scheme is based on the invariant energy quadratization approach.The MPFC equation is a damped wave equation,and to preserve an energy stability,it is necessary to introduce a pseudo energy,which all increase the difficulty of constructing numerical methods comparing with the phase field crystal(PFC)equation.Due to the severe time step restriction of explicit timemarchingmethods,we introduce the first order and second order semi-implicit schemes,which are proved to be unconditionally energy stable.In order to improve the temporal accuracy,the semi-implicit spectral deferred correction(SDC)method combining with the first order convex splitting scheme is employed.Numerical simulations of the MPFC equation always need long time to reach steady state,and then adaptive time-stepping method is necessary and of paramount importance.The schemes at the implicit time level are linear or nonlinear and we solve them by multigrid solver.Numerical experiments of the accuracy and long time simulations are presented demonstrating the capability and efficiency of the proposed methods,and the effectiveness of the adaptive time-stepping strategy.展开更多
Winter rape(Brassica napus L.)is better than other edible oil crops in China,but poor cold resistance is the key factor restricting its development.Hypocotyl length was found closely related to cold tolerance.The corr...Winter rape(Brassica napus L.)is better than other edible oil crops in China,but poor cold resistance is the key factor restricting its development.Hypocotyl length was found closely related to cold tolerance.The correlation between hypocotyl length and semi-lethal low temperature was significant,and the highest correlation between hypocotyl length and LT50 of autumn sowing was 0.9557.When the hypocotyl were treated at low temperature,the cells were seriously damaged and formed cavity structures,with cell walls seriously damaged or merged into each other.The positive regulation gene of hypocotyl length in resistant line of VHTSG 10 was identified as HY5(transcription factor HY5-like)by qPCR,and bZIP transcription factor was found to be its conserved domain.Fused gene by GFP and HY5 from VHTSG 10 was transient transferred into Nicotiana benthamiana cells.Corresponding to the 35S:GFP widely distributed in plasma membrane of leaf epidermis,the fusion protein 35S:HY5-GFP was mainly distributed in nucleus.Thus we regarded BnHY5 gene is a key gene related to cold tolerance and hypocotyl length in B.napus.展开更多
基金Research of R.Guo is supported by NSFC grant No.11601490Research of Y.Xu is supported by NSFC grant No.11371342,11626253,91630207.
文摘In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)equation.In which,the first order linear scheme is based on the invariant energy quadratization approach.The MPFC equation is a damped wave equation,and to preserve an energy stability,it is necessary to introduce a pseudo energy,which all increase the difficulty of constructing numerical methods comparing with the phase field crystal(PFC)equation.Due to the severe time step restriction of explicit timemarchingmethods,we introduce the first order and second order semi-implicit schemes,which are proved to be unconditionally energy stable.In order to improve the temporal accuracy,the semi-implicit spectral deferred correction(SDC)method combining with the first order convex splitting scheme is employed.Numerical simulations of the MPFC equation always need long time to reach steady state,and then adaptive time-stepping method is necessary and of paramount importance.The schemes at the implicit time level are linear or nonlinear and we solve them by multigrid solver.Numerical experiments of the accuracy and long time simulations are presented demonstrating the capability and efficiency of the proposed methods,and the effectiveness of the adaptive time-stepping strategy.
基金Longdong College youth Science and technology innovation project(XYZK2106)the Agriculture Research System Gansu Province(GARS-TSZ-1)+2 种基金Agriculture Research System of China(CARS-12)Study on variety substitution and key technology of cold resistance and high yield of winter rape(GSLK-2021-12)the National Natural Science Foundation of China(31860388)。
文摘Winter rape(Brassica napus L.)is better than other edible oil crops in China,but poor cold resistance is the key factor restricting its development.Hypocotyl length was found closely related to cold tolerance.The correlation between hypocotyl length and semi-lethal low temperature was significant,and the highest correlation between hypocotyl length and LT50 of autumn sowing was 0.9557.When the hypocotyl were treated at low temperature,the cells were seriously damaged and formed cavity structures,with cell walls seriously damaged or merged into each other.The positive regulation gene of hypocotyl length in resistant line of VHTSG 10 was identified as HY5(transcription factor HY5-like)by qPCR,and bZIP transcription factor was found to be its conserved domain.Fused gene by GFP and HY5 from VHTSG 10 was transient transferred into Nicotiana benthamiana cells.Corresponding to the 35S:GFP widely distributed in plasma membrane of leaf epidermis,the fusion protein 35S:HY5-GFP was mainly distributed in nucleus.Thus we regarded BnHY5 gene is a key gene related to cold tolerance and hypocotyl length in B.napus.
