Based on the assumption that solute transport in a semi-infinite soil columnor in a field soil profile can be described by the boundary-layer method, an analytical solution ispresented for the advance of a solute fron...Based on the assumption that solute transport in a semi-infinite soil columnor in a field soil profile can be described by the boundary-layer method, an analytical solution ispresented for the advance of a solute front with time. The traditional convection-dispersionequation (CDE) subjected to two boundary conditions: 1) at the soil surface (or inlet boundary) and2) at the solute front, was solved using a Laplace transformation. A comparison of residentconcentrations using a boundary-layer method and an exact solution (in a semi-infinite-domain)showed that both were in good agreement within the range between the two boundaries. This led to anew method for estimating solute transport parameters in soils, requiring only observation ofadvance of the solute front with time. This may be corroborated visually using a tracer solutionwith marking-dye or measured utilizing time domain reflectometry (TDR). This method is applicable toboth laboratory soil columns and field soils. Thus, it could be a step forward for modeling solutetransport in field soils and for better understanding of the transport processes in soils.展开更多
Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Eucl...Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.展开更多
基金Project supported by the National Key Basic Research Support Foundation of China (No. 2000018605) the National Natural Science Foundation of China (Nos. 40025106 and 40371060).
文摘Based on the assumption that solute transport in a semi-infinite soil columnor in a field soil profile can be described by the boundary-layer method, an analytical solution ispresented for the advance of a solute front with time. The traditional convection-dispersionequation (CDE) subjected to two boundary conditions: 1) at the soil surface (or inlet boundary) and2) at the solute front, was solved using a Laplace transformation. A comparison of residentconcentrations using a boundary-layer method and an exact solution (in a semi-infinite-domain)showed that both were in good agreement within the range between the two boundaries. This led to anew method for estimating solute transport parameters in soils, requiring only observation ofadvance of the solute front with time. This may be corroborated visually using a tracer solutionwith marking-dye or measured utilizing time domain reflectometry (TDR). This method is applicable toboth laboratory soil columns and field soils. Thus, it could be a step forward for modeling solutetransport in field soils and for better understanding of the transport processes in soils.
基金Project(JSPS.KAKENHI22560451) supported by the Japan Society for the Promotion of ScienceProject(69904003) supported by the National Natural Science Foundation of ChinaProject(YJ0267016) supported by the Advanced Ordnance Research Supporting Fund of China
文摘Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.
