A starquake mechanism for pulsar glitches is developed in the solid quark star model. It is found that the general glitch natures (i.e., the glitch amplitudes and the time intervals) could be reproduced if solid quark matter, with high baryon density but low temperature, has properties of shear modulus l ¼ 10 30-34 erg/cm 3 and critical stress r c ¼ 10 18$24 erg/cm 3 . The post-glitch behavior may represent a kind of damped oscillations.

We study the finite-size effects, like the surface and Coulomb energies, on the hadron-quark mixed phase in neutron stars. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions, which are different from the Gibbs conditions without finite-size effects. We employ the relativistic mean-field model to describe the hadronic phase, while the Nambu-Jona-Lasinio model with vector interactions is used for the quark phase. It is found that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those of the Gibbs and Maxwell constructions.We show that a massive star may contain a mixed phase core and its size depends on the surface tension of the hadron-quark interface and the vector coupling between quarks. The repulsive vector interaction in the Nambu-Jona-Lasinio model can stiffen the equation of state of quark matter, and therefore, delay the phase transition and increase the maximum mass of neutron stars.

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We examine the effects of the isovector-vector coupling and hypercharge-vector coupling in quark matter on hadron-quark coexistence in neutron-star matter. The relativistic mean field theory with the TM1 parameter set and an extended TM1 parameter set are used to describe hadronic matter, and the Nambu-Jona-Lasinio model with scalar, isoscalar-vector, isovector-vector and hyperchargevector couplings is used to describe deconfined quark matter. The hadron-quark phase transition is constructed via the Gibbs conditions for phase equilibrium. The isovector-vector and hyperchargevector couplings in quark matter enhance the symmetry energy and hypercharge symmetry energy in neutron-star matter, while their effects are found to be suppressed at high densities by the strange quarks. As a result, the hadron-quark mixed phase shrinks with only isovector-vector coupling and moves to higher density with isovector-vector and hypercharge-vector couplings. The maximum mass of neutron-star increases slightly with isovector-vector and hypercharge-vector couplings.