  We use very large cosmological Smoothed-Particle-Hydrodynamics simulations to
study the properties of high redshift Lyman-alpha emitters (LAEs). We identify
star-forming galaxies at z=3.1 in a cosmological volume of 100 h^-1Mpc on a
side. We develop a phenomenological model of absorption, scattering and escape
of Lyman-alpha photons on the assumption that the clumpiness of the
inter-stellar medium in a galaxy is correlated with the larger scale
substructure richness. The radiative transfer effect proposed by Neufeld (1991)
allows a large fraction of Lyman-alpha photons to escape from a clumpy galaxy
even if it contains a substantial amount of dust. Our model reproduces, for the
first time, all of the following observed properties of LAEs at z=3.1: the
angular correlation function, ultra-violet and Lyman-alpha luminosity
functions, and the equivalent width distribution. A simple model that takes
only dust absorption into account fails in matching the observational data,
suggesting that the kind of effect we consider is needed. Our model also
predicts a bimodal age distribution for LAEs. There are old, massive and dusty
LAEs, similar to recently found high redshift LAEs. The large LAEs have escape
fractions of Lyman-alpha photons of f_esc ~ 0.05-0.1.
