Principal coordinates and principal velocity gradient tensor decomposition

Helmholtz velocity decomposition and Cauchy-Stokes tensor decomposition have been widely accepted as the foundation of fluid kinematics for a long time.However,there are some problems with these decompositions which cannot be ignored.Firstly,Cauchy-Stokes decomposition itself is not Galilean invariant which means under different coordinates,the stretching(compression)and deformation are quite different.Another problem is that the anti-symmetric part of the velocity gradient tensor is not the proper quantity to represent fluid rotation.To show these two drawbacks,two counterexamples are given in this paper.Then“principal coordinate”and“principal decomposition”are introduced to solve the problems of Helmholtz decomposition.An easy way is given to find the Principal decomposition which has the property of Galilean invariance.

Combining conservation tillage with nitrogen fertilization promotes maize straw decomposition by regulating soil microbial community and enzyme activities

Straw return can effectively improve farmland soil microenvironment and fertility.However,excessive straw in the topsoil adversely affects seed germination and crop growth.At present,the characteristics and key driving factors of straw decomposition in dry farmlands are unclear.Based on the interactions between tillage practices including zero tillage(ZT),chisel tillage(CT),and plow tillage(PT)and nitrogen(N)fertilization,i.e.,low N(N1,180 kg ha^(-1)),normal N(N2,240 kg ha^(-1)),and high N(N3,300 kg ha^(-1)),quantitative polymerase chain reaction technology and an enzymatic detection kit were used to investigate the effects of key straw C-degrading enzyme activities and microbial abundance in soil on maize straw decomposition during the growth period of winter wheat in the winter wheat/summer maize double cropping system in a dry farmland of the Loess Plateau,China.Between 2018 and 2020,ZT and CT significantly increased winter wheat yield(by 10.94%and 12.79%,respectively)and straw decomposition velocity(by 20%and 26.67%,respectively),compared with PT.Compared to N1 and N3,N2 significantly increased wheat yield(by 4.65%and 5.31%,respectively)and straw decomposition velocity(by 26.33%and 13.21%,respectively).The partial least squares pathway modelling showed significant positive direct effects of soil moisture,NO3-,NH4+,total N,bacteria,and cellulase,laccase,and xylanase activities on straw decomposition,while soil pH,fungi,and Actinomycetes had significant negative direct effects.Overall,conservation tillage(ZT and CT)combined with N2 was beneficial for straw decomposition in the drylands of the Loess Plateau and improved straw resource utilization and basic soil fertility.The results of the study clarified the key drivers of straw decomposition in dry farmlands and provided new ideas for developing updated soil management practices and adaptive N application strategies to promote the resource utilization of straw and achieve the goals of carbon peaking and carbon neutrality.