Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoff systems is studied and the definition and criteria are given. In view of the invariance of rotational relativist...Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoff systems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic Pfaff Birkhoff D'Alembert principle under the infinitesimal transformations of groups, the theory of Noether symmetries of rotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noether symmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.展开更多
The rebound behaviors of droplets impacting on a self-fabricated superhydrophobic brass surface （WCA=I64.5°） were ob- served and studied by using high-speed-camera. In accordance with energy conversion, theoret...The rebound behaviors of droplets impacting on a self-fabricated superhydrophobic brass surface （WCA=I64.5°） were ob- served and studied by using high-speed-camera. In accordance with energy conversion, theoretical analysis of different behav- iors and rebound mechanism were given. At lower velocities, three behaviors in different velocity ranges were observed： par- tial rebounding, entire rebounding and ejecting during rebounding. At higher velocities, such two behaviors as rebound after splashing and rebound, ejecting after splashing, occurred alternately and exhibited certain periodicity. A function to predict the critical impact velocity is derived from energy conservation condition, and the prediction values tally with the experimental values, with the maximum relative error about 14%.展开更多
文摘Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoff systems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic Pfaff Birkhoff D'Alembert principle under the infinitesimal transformations of groups, the theory of Noether symmetries of rotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noether symmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.
基金supported by The National Natural Science Foundation of China (Grant No.51109178)Science and Technology Innovation Foundation of NWPU (Grant No.JC20120218)
文摘The rebound behaviors of droplets impacting on a self-fabricated superhydrophobic brass surface （WCA=I64.5°） were ob- served and studied by using high-speed-camera. In accordance with energy conversion, theoretical analysis of different behav- iors and rebound mechanism were given. At lower velocities, three behaviors in different velocity ranges were observed： par- tial rebounding, entire rebounding and ejecting during rebounding. At higher velocities, such two behaviors as rebound after splashing and rebound, ejecting after splashing, occurred alternately and exhibited certain periodicity. A function to predict the critical impact velocity is derived from energy conservation condition, and the prediction values tally with the experimental values, with the maximum relative error about 14%.
