On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the thi...On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.展开更多
Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic...Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.展开更多
The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate s...The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.展开更多
As for many post-soviet countries, Kazakhstan’s building code for seismic design was based on a deterministic approach. Recently, Kazakhstan seismologists are engaged to adapt the PSHA(probabilistic hazard assessment...As for many post-soviet countries, Kazakhstan’s building code for seismic design was based on a deterministic approach. Recently, Kazakhstan seismologists are engaged to adapt the PSHA(probabilistic hazard assessment) procedure to the large amount of available geological, geophysical and tectonic Kazakh data and to meet standard requirements for the Eurocode 8. The new procedure has been used within National projects to develop the Probabilistic GSZ(General Seismic Zoning) maps of the Kazakhstan territory and the SMZ(Probabilistic Seismic Microzoning) maps of Almaty city. They agree with the seismic design principles of Eurocode 8 and are expressed in terms of not only seismic intensity,but also engineering parameters(peak ground acceleration PGA). The whole packet of maps has been developed by the Institute of Seismology, together with other Kazakhstan Institutions. Our group was responsible for making analysis in PGA. The GSZ maps and hazard assessment maps for SMZ in terms of PGA for return periods 475 and 2475 years are considered in the article.展开更多
Within the seasonal-annual timeseale,there exists an angular momentum conservative exchange relationship be- tween the solid earth and the atmosphere,and their angular momentum exchange not only can cause variations i...Within the seasonal-annual timeseale,there exists an angular momentum conservative exchange relationship be- tween the solid earth and the atmosphere,and their angular momentum exchange not only can cause variations in length-of-day(LOD)but also can express anomalies in atmospheric general circulation.Therefore,their angular mo- mentum exchange mechanism should be introduced into the general circulation model. Considering the angular momentum anomalous exchange caused by the air-earth interface friction effect,a whole-layer atmospheric motion equation is derived in this paper including the earth spin anomalous friction force parameterized by using the change in the earth rotation rate.Through analysing the equation,it shows that the magni- tude of the earth spin anomalous friction force is the same as that of Coriolis force on seasonal-annual timescale.展开更多
This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its c...This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.展开更多
The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and clima...The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and climate. It is necessary to carry out some studiesof basic theory. Based on the stationary external forcings, Chou studied the adjustment of the nonlinear atmospheric system tending to forcings in R^n. Then these resultswere extended to the infinite dimensional Hilbert space. For the real atmospheric system,展开更多
From the large-scale equations of atmospheric motion, we investigated the long-time behaviour of atmospheric system forcing by exterior steady sources. Firstly, we established the fundamental functional space and oper...From the large-scale equations of atmospheric motion, we investigated the long-time behaviour of atmospheric system forcing by exterior steady sources. Firstly, we established the fundamental functional space and operator equations, and then demonstrated the existence and uniqueness theorems of solutions. Based on these results, the existence of the bounded global absorbing set and invariant set in it were discussed. Finally, the nonlinear adjustment process to exterior sources was revealed.展开更多
基金Project supported by the National Natural Science Foundation of China (Major Program of the Tenth Five-Year Plan) (No.90411006).
文摘On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typ- icality and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third-kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type ofproblems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.
基金Project supported by the National Natural Science Foundation of China (Nos.40175014, 90411006)the Science Foundation of Shanghai Municipal Commission of Science and Technology(No.02DJ14032)
文摘Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.
基金Project supported by the National Natural Science Foundation of China(Nos.40175014,90411006)
文摘The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.
基金"Development of the Map of General Seismic Zoning in the Territory of the Republic of Kazakhstan" (state registration 0113RK01142)"Development of the map of Seismic Microzoning of the Territory of Almaty City"(state registration 0115RK02701)funded within the state funding
文摘As for many post-soviet countries, Kazakhstan’s building code for seismic design was based on a deterministic approach. Recently, Kazakhstan seismologists are engaged to adapt the PSHA(probabilistic hazard assessment) procedure to the large amount of available geological, geophysical and tectonic Kazakh data and to meet standard requirements for the Eurocode 8. The new procedure has been used within National projects to develop the Probabilistic GSZ(General Seismic Zoning) maps of the Kazakhstan territory and the SMZ(Probabilistic Seismic Microzoning) maps of Almaty city. They agree with the seismic design principles of Eurocode 8 and are expressed in terms of not only seismic intensity,but also engineering parameters(peak ground acceleration PGA). The whole packet of maps has been developed by the Institute of Seismology, together with other Kazakhstan Institutions. Our group was responsible for making analysis in PGA. The GSZ maps and hazard assessment maps for SMZ in terms of PGA for return periods 475 and 2475 years are considered in the article.
基金This work is supported by the National Natural Science Foundation of China(No.493752477)the Doctorial Program Foundation of the Institution of Higher Education.
文摘Within the seasonal-annual timeseale,there exists an angular momentum conservative exchange relationship be- tween the solid earth and the atmosphere,and their angular momentum exchange not only can cause variations in length-of-day(LOD)but also can express anomalies in atmospheric general circulation.Therefore,their angular mo- mentum exchange mechanism should be introduced into the general circulation model. Considering the angular momentum anomalous exchange caused by the air-earth interface friction effect,a whole-layer atmospheric motion equation is derived in this paper including the earth spin anomalous friction force parameterized by using the change in the earth rotation rate.Through analysing the equation,it shows that the magni- tude of the earth spin anomalous friction force is the same as that of Coriolis force on seasonal-annual timescale.
基金supported by the National Natural Science Foundation of China(Grant No.10471003)Foundation for Authors Awarded Excellent Ph.D.Dissertation.
文摘This paper gives probabilistic expressions of theminimal and maximal positive solutions of the partial differential equation -1/2△v(x) + γ(x)v(x)α = 0 in D, where D is a regular domain in Rd(d ≥ 3) such that its complement Dc is compact, γ(x) is a positive bounded integrable function in D, and 1 ＜α≤ 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.
基金State Key Research Project on Dynamics and Predictive Theory of the Climate and the Doctor's Foundation of State Education Committee.
文摘The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and climate. It is necessary to carry out some studiesof basic theory. Based on the stationary external forcings, Chou studied the adjustment of the nonlinear atmospheric system tending to forcings in R^n. Then these resultswere extended to the infinite dimensional Hilbert space. For the real atmospheric system,
文摘From the large-scale equations of atmospheric motion, we investigated the long-time behaviour of atmospheric system forcing by exterior steady sources. Firstly, we established the fundamental functional space and operator equations, and then demonstrated the existence and uniqueness theorems of solutions. Based on these results, the existence of the bounded global absorbing set and invariant set in it were discussed. Finally, the nonlinear adjustment process to exterior sources was revealed.
