We propose a new type of dark energy （DE） model, in which the equation of state of DE wae is a simple function of the fractional energy density Ωde instead of the redshift z. We assume three DE models of this type,...We propose a new type of dark energy （DE） model, in which the equation of state of DE wae is a simple function of the fractional energy density Ωde instead of the redshift z. We assume three DE models of this type, and fit them with present observations to get constraints of DE, which are also compared with the CPL model. It is shown that a suitable wda,（Ωde） model can give smaller X2 or smaller errors of wde than that of the CPL model. This new type of DE model can help to study the essential properties and nature of DE.展开更多
Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equati...Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equations that is derived from the standard deterministic ordinary differential equation by adding the process variability to the growth dynamic. Age-diameter varying height model was deduced using a two-dimensional stochastic Gompertz shape process. Another focus of the article is the investigation of normal cop- ula procedure, when the tree diameter and height are governed by univariate stochastic Gompertz shape processes. The advantage of the stochastic differential equation method- ology is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects more complex than commonly used fixed effect models. An analysis of 900 Scots pine （Pinus sylvestris） trees provided the data for this study.展开更多
Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiqui- tous in applications in contemporary science and engin...Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiqui- tous in applications in contemporary science and engineering where the statistical ensemble prediction and the real time filtering/state estimation are needed despite the underlying complexity of the system. Statistically exactly solvable test models have a crucial role to provide firm mathematical underpinning or new algorithms for vastly more complex scien- tific phenomena. Here, a class of statistically exactly solvable non-Gaussian test models is introduced, where a generalized Feynman-Ka~ formulation reduces the exact behavior of conditional statistical moments to the solution to inhomogeneous Fokker-Planck equations modified by linear lower order coupling and source terms. This procedure is applied to a test model with hidden instabilities and is combined with information theory to address two important issues in the contemporary statistical prediction of turbulent dynamical systems： the coarse-grained ensemble prediction in a perfect model and the improving long range forecasting in imperfect models. The models discussed here should be use- ful for many other applications and algorithms for the real time prediction and the state estimation.展开更多
基金Supported in part by the National Natural Science Foundation of China under Grant No. 11147186Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ12A05004 and Grant from Hangzhou Normal University
文摘We propose a new type of dark energy （DE） model, in which the equation of state of DE wae is a simple function of the fractional energy density Ωde instead of the redshift z. We assume three DE models of this type, and fit them with present observations to get constraints of DE, which are also compared with the CPL model. It is shown that a suitable wda,（Ωde） model can give smaller X2 or smaller errors of wde than that of the CPL model. This new type of DE model can help to study the essential properties and nature of DE.
文摘Height diameter models are classically analyzed by fixed or mixed linear and non-linear regression models. In order to possess the among-plot variability, we propose the method- ology of stochastic differential equations that is derived from the standard deterministic ordinary differential equation by adding the process variability to the growth dynamic. Age-diameter varying height model was deduced using a two-dimensional stochastic Gompertz shape process. Another focus of the article is the investigation of normal cop- ula procedure, when the tree diameter and height are governed by univariate stochastic Gompertz shape processes. The advantage of the stochastic differential equation method- ology is that it analyzes a residual variability, corresponding to measurements error, and an individual variability to represent heterogeneity between subjects more complex than commonly used fixed effect models. An analysis of 900 Scots pine （Pinus sylvestris） trees provided the data for this study.
基金Project supported by the Office of Naval Research (ONR) Grants (No. ONR DRI N00014-10-1-0554)the DOD-MURI award "Physics Constrained Stochastic-Statistical Models for Extended Range Environmental Prediction"
文摘Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiqui- tous in applications in contemporary science and engineering where the statistical ensemble prediction and the real time filtering/state estimation are needed despite the underlying complexity of the system. Statistically exactly solvable test models have a crucial role to provide firm mathematical underpinning or new algorithms for vastly more complex scien- tific phenomena. Here, a class of statistically exactly solvable non-Gaussian test models is introduced, where a generalized Feynman-Ka~ formulation reduces the exact behavior of conditional statistical moments to the solution to inhomogeneous Fokker-Planck equations modified by linear lower order coupling and source terms. This procedure is applied to a test model with hidden instabilities and is combined with information theory to address two important issues in the contemporary statistical prediction of turbulent dynamical systems： the coarse-grained ensemble prediction in a perfect model and the improving long range forecasting in imperfect models. The models discussed here should be use- ful for many other applications and algorithms for the real time prediction and the state estimation.
