Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

In our previous work [Phys. Rev. A 85 （2012） 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann-Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition （ESQPT） in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.

Study on the instantaneous protection reliability of low voltage circuit breakers

This paper outlines the significance of enhancing the instantaneous protection reliability of low voltage circuit breakers and describes their main failure modes. The instantaneous failure mechanism of low voltage circuit breakers was analyzed so that measures to improve instantaneous protection reliability can be determined. Furthermore, the theory of the instantaneous characteristics calibration device for low voltage circuit breakers and the method of eliminating the non-periodic component of test current are given in detail. Finally, the test results are presented.

Evolution of TCP Phase During Long Term Thermal Exposure in Several Re-Containing Single Crystal Superalloys

The application and component designs of single crystal superalloys are restricted by the precipitation of topologically closed packed(TCP)phases,which can deteriorate the microstructural stability of the alloys severely.Limited researches concerning the type and morphology evolution of TCP phases under elevated temperature conditions have been reported previously.In the present work,three Re-containing single crystal alloys were designed to investigate TCP phase evolution via long term isothermal exposure tests at 1120℃while the effects of Re on the microstructural characteristic and elements segregation were also clarified.The results showed that the addition of Re increased the instability of the alloys and the volume fraction of the TCP phases exceeded 5 vol%when the Re content reached 3 wt%.The increasing Re content had also raised the precipitation temperature of TCP phases but it did not change the type of them after long term aging;all the TCP particles were identified asμphase in this study.Moreover,the elements segregation became considerably serious as Re addition increased constantly,which brought about various morphologies of theμphase in the experimental alloys.In particular,the rod-like and needle-likeμphases demonstrated the typical orientation withinγmatrix while the blockyμphase was dispersedly distributed in the space.No specific orientation relationship could be observed in theμphase when the addition of Re exceeded certain threshold value.

The precipitation and effect of topologically close-packed phases in Ni-based single crystal superalloys

The precipitation of topologically close-packed(TCP)phases is the result of microstructure instabilities of Ni-based superalloys.This review seeks to comprehensively collate all the available information on TCP phases in SX superalloys based on the latest findings.First,the thermodynamics and kinetics of the TCP phase precipitation are introduced.Meanwhile,the morphology,composition and orientation of TCP phases and their sequential transformation are summarized in detail.Further,the factors affecting the precipitation of these phases are sorted out.Besides,the proposed damage mechanisms of TCP phases are listed.Finally,several control and prediction methods of the TCP phase precipitation are reviewed,so the alloy designer can better balance the relationship between microstructure stabilities and properties of the superalloy.