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This paper introduces the finding of some chaotic attractors in a kind of n-dimensional autonomous hybrid system, which is realized via applying some discontinuous state feedback to a kind of n linear differential system. And a constructive theorem is proposed for generalized synchronization related to the above chaotic hybrid systems. Examples are presented for illustrating the methods.

The hardness and ideal strength of P-carbon, i.e., a new carbon phase for the cold-compressed carbon with an orthogonal structure recently proposed and named as P-carbon, are investigated by means of first-principles calculations. The strength calculations reveal that the failure mode in P-carbon is dominated by the tensile type. The ideal tensile strength of P-carbon is calculated to be 76.7 GPa in the [001] direction, which is higher than that of the previously known most stable Z-carbon, of 71.4 GPa. Meanwhile, the theoretical Vickers hardness of P-carbon is estimated as 89 GPa, which is comparable with that of diamond. Especially, two types of bonds in P-carbon with hardness values of 114 GPa and 105 GPa are significantly stronger than those of diamond. The results provide insight into exploration of the ultra-hard P-carbon for potentially technological applications.

The Rapid Cycling Synchrotron (RCS) is a key component of the China Spallation Neutron Source (CSNS). For this type of high intensity proton synchrotron, the chromaticity, space charge effects, and magnetic field tracking errors between the quadrupoles and the dipoles can induce beta function distortion and tune shift, and induce resonances. In this paper, the combined effects of chromaticity, magnetic field tracking errors and space charge on beam dynamics at CSNS/RCS are studied systemically. 3-D simulations with different magnetic field tracking errors are performed by using the code ORBIT, and the simulation results are compared with the case without tracking errors.