Lie symmetries and conserved quantities for a two-dimentional nonlinear diffusion equation of concentration

The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation ot concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.

Effect and Risk Assessment of Animal Manure Pollution on Huaihe River Basin, China

Currently the deteriorated water quality for Huaihe River Basin(HRB) in China was still serious because of the negative influence multiple pollution sources including animal manure. However, little attention was paid to the potential risk of animal manure for farmland and water quality of HRB. This study was quantified and forecasted animal manure risk and its spatiotemporal variations in HRB from 2008 to 2018, through pollution discharge coefficient method and pollution load calculation, combined with kriging interpolation method of ArcGIS technology, based on statistics principle. All the data were originated from livestock and poultry breeding in HRB from 2008 to 2018. The future risk of farmland and water environment in HRB was further forecasted. The results indicated that the livestock and poultry manure has become a key pollution source causing a negative influence on farmland and water quality owing to a large amount of animal manure production without efficient recycle utilization. The chemical oxygen demand(COD) and total nitrogen(TN) discharge of animal manure in HRB almost accounted for 17.00% and 39.00% of the whole COD and TN discharge in China. The diffusion concentration of TN and TP in those regions of Shangqiu, Zhoukou, Heze, Zhumadian, Luohe, Jining, Xuchang,Kaifeng, Taian and Zhengzhou of HRB has exceeded the threshold value 10.00 mg/L of TN and 0.08 mg/L of TP, causing water eutrophication and cancer villages. The assessment of farmland and water quality risk revealed that Zhumadian, Zhoukou, Shangqiu, Taian, Jining, Heze, Linyi and Rizhao belonged to high risk areas in HRB, which were still obtained high farmland and water quality risk index in 2030. The results provided insight into an important significance of sustainable balance of livestock and poultry development and ecosystem in HRB.

Dynamic Mechanism of Migmatization in the Dabie Complex, Northeastern Hubei, China

On the basis of the detailed field work, compositions and contents of plagioclase and K - feldspar,determination of ordering degree, statistical analysis of plagioclase elongation index, mass-balance calculation and mineral spatial distribution and geochemistry, it is concluded that the migmatites in the Dabie complex are characterized by the presence of thermocenters. There are regular changes in mineral character in the migmatites from the centers outwards. The dominant genetic mechanism is anatexis and metasomatism, whose intensities decrease from the centers outwards. Finally, according to the simulated experiment on Liesegang' s rings and non-linear dynamics (dissipative structure theory), the dynamic mechanism of migmatization is profoundly expouded as consisting of the early-stage metasomatism induced by the thermal anomaly, the cardinal-stage anatexis induced by the early-stage matasomatism and finally the last-stage post-anatexis metasomatism.

Types,Concentration,Diffusion and Spatial Structure Evolution of Natural Gas Resource Flow in China

This paper analyzed the development of different types of natural gas flow zones in China, and then di- vided all provinces into four flow types： non-flow zones, output centers, input centers and exchanging centers. Next, we analyzed the concentration and diffusion characteristics, current spatial pattern and evolution of source and terminal regions of natural gas resource flows. The numbers of non-flow zones, output centers, input centers and exchanging centers all stabilized during the Eleventh Five-Year Plan period. The number of output centers is small but the quantity of flow is large. The number of input centers is large and they are widely distributed. Generally speaking, it presents a significant characteristic of centralized output and dispersed input in geographic space. The current situation for China＇s natural gas output source has random distribution characteristics, but the terminal re- gions of natural gas flow have strong positive spatial correlation, presenting a significant spatial agglomeration pattern. Shandong, Jiangsu, Zhejiang and Shanghai have a high-high agglomeration mode, but Yunnan, Sichuan, Tibet, Qinghai and Gansu have a low-low agglomeration output zones had three different stages： relatively stable mode. Spatial pattern changes in China＇ s natural gas from 2001-2003; moved northwestward, expanded in space, and widely dispersed during 2004-2006; and transferred to the east, spatially contracted and significantly concentrated during 2007-2011. Spatial pattern changes in China＇s natural gas input zones have two stages： ex- panded in east-west direction while contracted in north-south direction during 2001-2005; and relatively stable in spatial structure with intensification from 2006-2011.

Effects of elevated atmospheric CO_2 concentration and temperature on the soil profile methane distribution and diffusion in rice–wheat rotation system

The aim of this experiment was to determine the impacts of climate change on soil profile concentrations and diffusion effluxes of methane in a rice-wheat annual rotation ecosystem in Southeastern China. We initiated a field experiment with four treatments：ambient conditions（CKs）, CO2 concentration elevated to - 500 μmol/mol（FACE）,temperature elevated by ca. 2°C（T） and combined elevation of CO2 concentration and temperature（FACE ＋ T）. A multilevel sampling probe was designed to collect the soil gas at four different depths, namely, 7 cm, 15 cm, 30 cm and 50 cm. Methane concentrations were higher during the rice season and decreased with depth, while lower during the wheat season and increased with depth. Compared to CK, mean methane concentration was increased by 42%, 57% and 71% under the FACE, FACE ＋ T and T treatments, respectively, at the 7 cm depth during the rice season（p 〈 0.05）. Mean methane diffusion effluxes to the 7 cm depth were positive in the rice season and negative in the wheat season, resulting in the paddy field being a source and weak sink, respectively. Moreover, mean methane diffusion effluxes in the rice season were 0.94, 1.19 and 1.42 mg C/（m^2·hr） in the FACE,FACE ＋ T and T treatments, respectively, being clearly higher than that in the CK. The results indicated that elevated atmospheric CO2 concentration and temperature could significantly increase soil profile methane concentrations and their effluxes from a rice-wheat field annual rotation ecosystem（p 〈 0.05）.