  Kinetically constrained models (KCMs) have gained much interest as models
that assign the origins of interesting dynamic properties of supercooled
liquids to dynamical facilitation mechanisms that have been revealed in many
expreiments and numerical simulations. In this work, we investigate the dynamic
heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the
model that linearly interpolates between the strong-liquid like behavior and
the fragile-liquid like behavior by an asymmetry parameter b. When the
asymmetry parameter is sufficiently small, smooth fragile-to-strong transition
is observed both in the relaxation time and the diffusion constant. Using these
physical quantities, we investigate fractional Stokes-Einstein relations
observed in this model. When b is fixed, the system shows constant power law
exponent under the temperature change, and the exponent has the value between
that of the FA model and the East model. Furthermore, we investigate the
dynamic length scale of our systems and also find the crossover relation
between the relaxation time. We ascribe the competition between energetically
favored symmetric relaxation mechanism and entropically favored asymmetric
relaxation mechanism to the fragile-to-strong crossover behavior.
