Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condit...Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.展开更多
A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of varia...A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.展开更多
In this paper a mixed finite element method for the convection dominated diffusion problems with small parameter ε is presented,the effect of the parameter ε on the approximation error is considered and a su...In this paper a mixed finite element method for the convection dominated diffusion problems with small parameter ε is presented,the effect of the parameter ε on the approximation error is considered and a sufficient condition for optimal error estimates is derived.The paper also shows that under some conditions,the standard finite element method only gives a bounded solution,however the mixed finite element method gives a convergent one. Received March 1,1997. 1991 MR Subject Classification: 65N30,65M15.展开更多
Unresolved small-scale orographic（SSO） drags are parameterized in a regional model based on the Global/Regional Assimilation and Prediction System for the Tropical Mesoscale Model（GRAPES TMM）. The SSO drags are re...Unresolved small-scale orographic（SSO） drags are parameterized in a regional model based on the Global/Regional Assimilation and Prediction System for the Tropical Mesoscale Model（GRAPES TMM）. The SSO drags are represented by adding a sink term in the momentum equations. The maximum height of the mountain within the grid box is adopted in the SSO parameterization（SSOP） scheme as compensation for the drag. The effects of the unresolved topography are parameterized as the feedbacks to the momentum tendencies on the first model level in planetary boundary layer（PBL）parameterization. The SSOP scheme has been implemented and coupled with the PBL parameterization scheme within the model physics package. A monthly simulation is designed to examine the performance of the SSOP scheme over the complex terrain areas located in the southwest of Guangdong. The verification results show that the surface wind speed bias has been much alleviated by adopting the SSOP scheme, in addition to reduction of the wind bias in the lower troposphere. The target verification over Xinyi shows that the simulations with the SSOP scheme provide improved wind estimation over the complex regions in the southwest of Guangdong.展开更多
The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reyn...The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.展开更多
The analytical solutions of the PBL wind distribution under the equilibrium of four forces including both horizontal and vertical advections are obtained in this paper using small parameter method. Utilizing this simp...The analytical solutions of the PBL wind distribution under the equilibrium of four forces including both horizontal and vertical advections are obtained in this paper using small parameter method. Utilizing this simple PBL model, we also compute the wind spirals of a certain circular vortex over level ground and over a west-east ranged mountain, respectively. The results show that when there exsits large-scale orographic forcing,vertical advection may exert considerable influence on the wind distribution of PBL, the angle between geostrophic flow and surface wind, and the height of the top of PBL.展开更多
文摘Technical stability:allowing quantitative estimation of trajectory behavior of a dynamical system over a given time interval was considered. Based on a differential comparison principle and a basic monotonicity condition, technical stability relative to certain prescribed state constraint sets of a class of nonlinear time-varying systems with small parameters was analyzed by means of vector Liapunov function method. Explicit criteria of technical stability are established in terms of coefficients of the system under consideration. Conditions under which the technical stability of the system can be derived from its reduced linear time-varying (LTV) system were further examined, as well as a condition for linearization approach to technical stability of general nonlinear systems. Also, a simple algebraic condition of exponential asymptotic stability of LTV systems is presented. Two illustrative examples are given to demonstrate the availability of the presently proposed method.
基金supported by the National Natural Science Foundation of China (No. 10671070)the Fund for E-Institute of Shanghai Universities (No. E03004)the Open Research Fund Program of LGISEM(No. 05PJ14040)
文摘A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.
文摘In this paper a mixed finite element method for the convection dominated diffusion problems with small parameter ε is presented,the effect of the parameter ε on the approximation error is considered and a sufficient condition for optimal error estimates is derived.The paper also shows that under some conditions,the standard finite element method only gives a bounded solution,however the mixed finite element method gives a convergent one. Received March 1,1997. 1991 MR Subject Classification: 65N30,65M15.
基金supported by the National Natural Science Foundation of China(Grant Nos.41505084,41275053and 41461164006)the China Meteorological Administration Special Public Welfare Research Fund(Grant Nos.GYHY201406003 and GYHY201406009)+1 种基金the Guangdong Meteorological Service Project(Grant No.2015B01)the Guangdong Province Public Welfare Research and Capacity Construction Project(Grant No.2017B020218003)
文摘Unresolved small-scale orographic（SSO） drags are parameterized in a regional model based on the Global/Regional Assimilation and Prediction System for the Tropical Mesoscale Model（GRAPES TMM）. The SSO drags are represented by adding a sink term in the momentum equations. The maximum height of the mountain within the grid box is adopted in the SSO parameterization（SSOP） scheme as compensation for the drag. The effects of the unresolved topography are parameterized as the feedbacks to the momentum tendencies on the first model level in planetary boundary layer（PBL）parameterization. The SSOP scheme has been implemented and coupled with the PBL parameterization scheme within the model physics package. A monthly simulation is designed to examine the performance of the SSOP scheme over the complex terrain areas located in the southwest of Guangdong. The verification results show that the surface wind speed bias has been much alleviated by adopting the SSOP scheme, in addition to reduction of the wind bias in the lower troposphere. The target verification over Xinyi shows that the simulations with the SSOP scheme provide improved wind estimation over the complex regions in the southwest of Guangdong.
文摘The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.
文摘The analytical solutions of the PBL wind distribution under the equilibrium of four forces including both horizontal and vertical advections are obtained in this paper using small parameter method. Utilizing this simple PBL model, we also compute the wind spirals of a certain circular vortex over level ground and over a west-east ranged mountain, respectively. The results show that when there exsits large-scale orographic forcing,vertical advection may exert considerable influence on the wind distribution of PBL, the angle between geostrophic flow and surface wind, and the height of the top of PBL.
