A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and t...A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).展开更多
Based on Duan＇s topological current theory,we propose a novel approach to study the topological properties of topological defects in a two-dimensional complex vector order parameter system.This method shows explicitl...Based on Duan＇s topological current theory,we propose a novel approach to study the topological properties of topological defects in a two-dimensional complex vector order parameter system.This method shows explicitly the fine topological structure of defects.The branch processes of defects in the vector order parameter system have also been investigated with this method.展开更多
Background:The terminal branch orders of plant root systems are increasingly known as an ephemeral module.This concept is crucial to recognize belowground processes.However,it is unknown if root modules still exist af...Background:The terminal branch orders of plant root systems are increasingly known as an ephemeral module.This concept is crucial to recognize belowground processes.However,it is unknown if root modules still exist after they die?Methods:The decomposition patterns of the first five root orders were observed for 3 years using a branch-order classification,a litter-bag method and sequential sampling in a common subalpine tree species(Picea asperata)of southwestern China.Results:Two root modules were observed during the 3-year incubation.Among the first five branch orders,the first three order roots exhibited temporal patterns of mass loss,nutrients and stoichiometry distinct from their woody mother roots throughout the experimental period.This study,for the first time,reported the decomposition pattern of each individual root order and found a similar decomposition dynamic among ephemeral root branches in a forest tree species.Conclusions:Results from this study suggest that root modules may also exist after death,while more data are needed for confirmation.The findings may further advance our understanding of architecture-associated functional heterogeneity in the fine-root system and also improve our ability to predict belowground processes.展开更多
文摘A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).
基金Project supported by the National Natural Science Foundation of China (Grant No 10275030)Cuiying Project of Lanzhou University of China (Grant No 225000-582404)
文摘Based on Duan＇s topological current theory,we propose a novel approach to study the topological properties of topological defects in a two-dimensional complex vector order parameter system.This method shows explicitly the fine topological structure of defects.The branch processes of defects in the vector order parameter system have also been investigated with this method.
基金funded by the National Natural Science Foundation of China(Nos.32071745,31870602,31800519 and 31901295)Program of Sichuan Excellent Youth Sci-Tech Foundation(No.2020JDJQ0052)the National Key Research and Development Program of China(Nos.2016YFC0502505and 2017YFC0505003)。
文摘Background:The terminal branch orders of plant root systems are increasingly known as an ephemeral module.This concept is crucial to recognize belowground processes.However,it is unknown if root modules still exist after they die?Methods:The decomposition patterns of the first five root orders were observed for 3 years using a branch-order classification,a litter-bag method and sequential sampling in a common subalpine tree species(Picea asperata)of southwestern China.Results:Two root modules were observed during the 3-year incubation.Among the first five branch orders,the first three order roots exhibited temporal patterns of mass loss,nutrients and stoichiometry distinct from their woody mother roots throughout the experimental period.This study,for the first time,reported the decomposition pattern of each individual root order and found a similar decomposition dynamic among ephemeral root branches in a forest tree species.Conclusions:Results from this study suggest that root modules may also exist after death,while more data are needed for confirmation.The findings may further advance our understanding of architecture-associated functional heterogeneity in the fine-root system and also improve our ability to predict belowground processes.
