A new easy method has been presented to calculate the variable intervals corresponding to the stable univariant curves and to discriminate the stabilities of invariant points. This method and the one reported previous...A new easy method has been presented to calculate the variable intervals corresponding to the stable univariant curves and to discriminate the stabilities of invariant points. This method and the one reported previously constitute a simple and universal theory for the computer-plotting of the equilibrium phase diagrams of a multisystem—sign function matrix (SFM) discrimination method. Its main steps are: determining the stable univariant scheme according to the derivative (or difference) of AIG m ; grouping the univariant curves by comparisons of the mutual relations among them; determining the existing intervals of the variables for the stable curves by comparisons of coordinate values of the curves about the invariant point; determining the stabilities of invariant points by comparisons of relations between the common curves and the invariant points. This method is suitable for any kind of phase diagram of closed or open systems in a phase diagram “space” with either 2 or more than 2 dimensions.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.4907017849773200).
文摘A new easy method has been presented to calculate the variable intervals corresponding to the stable univariant curves and to discriminate the stabilities of invariant points. This method and the one reported previously constitute a simple and universal theory for the computer-plotting of the equilibrium phase diagrams of a multisystem—sign function matrix (SFM) discrimination method. Its main steps are: determining the stable univariant scheme according to the derivative (or difference) of AIG m ; grouping the univariant curves by comparisons of the mutual relations among them; determining the existing intervals of the variables for the stable curves by comparisons of coordinate values of the curves about the invariant point; determining the stabilities of invariant points by comparisons of relations between the common curves and the invariant points. This method is suitable for any kind of phase diagram of closed or open systems in a phase diagram “space” with either 2 or more than 2 dimensions.
