  We perform numerical simulations of the jamming transition of non-spherical
particles in two dimensions. In particular, we systematically investigate how
the physical quantities at the jamming transition point behave when the shapes
of the particle deviate slightly from the perfect disks. For efficient
numerical simulation, we first derive an analytical expression of the gap
function, using the perturbation theory around the reference disks. Starting
from disks, we observe the effects of the deformation of the shapes of
particles by the $n$-th order term of the Fourier series $\sin(n\theta)$. We
show that the several physical quantities, such as the number of contacts, gap
distribution, and characteristic frequencies of the vibrational density of
states, show the power-law behaviors with respect to the linear deviation from
the reference disks. The power-law behaviors do not depend on $n$ and are fully
consistent with the mean-field theory of the jamming of non-spherical
particles. This result suggests that the mean-field theory holds very generally
for nearly spherical particles whose shape can be expressed by the Fourier
series.
