  Star formation in galaxies is inefficient, and understanding how star
formation is regulated in galaxies is one of the most fundamental challenges of
contemporary astrophysics. Radiative cooling, feedback from supernovae and
active galactic nuclei, large-scale dynamics and dissipation of turbulent
energy act over various time and spatial scales, and all regulate star
formation in a complex gas cycle. This paper presents the physics implemented
in a new semi-analytical model of galaxy formation and evolution: G.A.S.. The
fundamental underpinning of our new model is the development of a multi-phase
interstellar medium in which energy produced by supernovae and active galactic
nuclei maintains an equilibrium between the diffuse, hot, stable gas and a
cooler, clumpy, low-volume filling factor gas. The hot gas is susceptible to
thermal and dynamical instabilities. We include a description of how turbulence
leads to the formation of giant molecular clouds through an inertial turbulent
energy cascade. We explicitly model the evolution of the velocity dispersion at
different scales of the cascade and account for thermal instabilities in the
hot halo gas. We show that rapid and multiple exchanges between diffuse and
unstable gas phases strongly regulates star-formation rates in galaxies because
only a small fraction of the unstable gas is forming stars. For high mass
halos, cooling is naturally regulated by the growth of thermal instabilities,
so we do not need to implement strong AGN feedback. The characteristic
timescales describing the gas cycle are in good agreement with observations.
Results are in good agreement with the observed stellar mass function from
z=6.0 to z=0.5. Thermal instabilities and the cascade of turbulent energy in
the dense gas phase introduce a delay between gas accretion and star formation,
which keeps galaxy growth inefficient in the early Universe.
