  To understand the chirality selection in the biological organic system, a
simple lattice model of chemical reaction with molecular diffusion is proposed
and studied by Monte Carlo simulations. In addition to a simple stochastic
process of conversions between an achiral reactant A and chiral products, R and
S molecules, a nonlinear autocatalysis is incorporated by enhancing the
reaction rate from A to R (or S), when A is surrounded by more than one R (or
S) molecules. With this nonlinear autocatalysis, the chiral symmetry between R
and S is shown to be broken in a dense system. In a dilute solution with a
chemically inactive solvent, molecular diffusion accomplishes chirality
selection, provided that the initial concentration is higher than the critical
value.
