Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distributio...Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f（x）（it is a monotone increasing fractal function） and its some applications.展开更多
In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biol...In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biological and engineering sciences. A major component of this tool is a coupled chaotic dynamical system obtained by coupling two versions of the well-known Lorenz （1963） model with different time scales which differ by a certain time-scale factor. A tangent linear model and its adjoint are considered that correspond to a coupled chaotic system. The general idea of applying sensitivity measures （sensitivity functions） to coupled systems, emphasizing the data assimilation aspects, is explored as well by the forward sensitivity approach. For this purpose the set of sensitivity equations is derived from the nonlinear equations of the coupled dynamical system. To estimate the influence of model parameter uncertainties on the simulated state variables the relative error in the energy norm is used.展开更多
基金Foundation item： Supported by the Youth Science Foundation of Henan Normal University（521103）
文摘Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f（x）（it is a monotone increasing fractal function） and its some applications.
文摘In this paper, a numerical modeling tool is described which can be used to explore various aspects of four dimensional variational data assimilation and parameter estimation arising in geophysical, environmental, biological and engineering sciences. A major component of this tool is a coupled chaotic dynamical system obtained by coupling two versions of the well-known Lorenz （1963） model with different time scales which differ by a certain time-scale factor. A tangent linear model and its adjoint are considered that correspond to a coupled chaotic system. The general idea of applying sensitivity measures （sensitivity functions） to coupled systems, emphasizing the data assimilation aspects, is explored as well by the forward sensitivity approach. For this purpose the set of sensitivity equations is derived from the nonlinear equations of the coupled dynamical system. To estimate the influence of model parameter uncertainties on the simulated state variables the relative error in the energy norm is used.
