The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies f...The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.展开更多
A modification of central profile with trigonometric curve is proposed based on the theory of engagement of scroll compressor. General modification equations for central profile of a pair of scrolls are given and vari...A modification of central profile with trigonometric curve is proposed based on the theory of engagement of scroll compressor. General modification equations for central profile of a pair of scrolls are given and various modification patterns are discussed. The equidistant method is employed to calculate the volume of a sealed chamber and a set of general equations is represented. Modification parameters affecting geometric and dynamic property of a scroll compressor are analyzed systematically, and the relations between them are accurately determined. The condition for transforming a trigonometric curve modification into an arc-curve modification is explained. The conclusions can also be applied to other scroll fluid machines.展开更多
文摘The profile equations of geometric optics are described in a form invariant under the natural transformations of first order systems of partial differential equations. This allows us to prove that various strategies for computing profile equations are equivalent. We prove that if L generates an evolution on L2 the same is true of the profile equations. We prove that the characteristic polynomial of the profile equations is the localization of the characteristic polynomial of the background operator at （y, dφ（y）） where φ is the background phase. We prove that the propagation cones of the profile equations are subsets of the propagation cones of the background operator.
基金This project is supported by Provincial Natural Science Foundation of Gansu(No.ZS032-B25-026).
文摘A modification of central profile with trigonometric curve is proposed based on the theory of engagement of scroll compressor. General modification equations for central profile of a pair of scrolls are given and various modification patterns are discussed. The equidistant method is employed to calculate the volume of a sealed chamber and a set of general equations is represented. Modification parameters affecting geometric and dynamic property of a scroll compressor are analyzed systematically, and the relations between them are accurately determined. The condition for transforming a trigonometric curve modification into an arc-curve modification is explained. The conclusions can also be applied to other scroll fluid machines.
