  It depends on the state of matter at supra-nuclear density to model pulsar's
structure, which is unfortunately not certain due to the difficulties in
physics. In cold quark matter at realistic baryon densities of compact stars
(with an average value of $\sim 2-3\rho_0$), the interaction between quarks is
so strong that they would condensate in position space to form quark-clusters.
We argue that quarks in quark stars are grouped in clusters, then we apply two
phenomenological models for quark stars, the polytropic model and Lennard-Jones
model. Both of the two models have stiffer EoS, and larger maximum mass for
quark stars (larger than 2 $M_\odot$). The gravitational energy releases during
the AIQ process could explain the observed energy of three supergiant flares
from soft gamma-ray repeaters ($\sim 10^{47}$ ergs).
