  Major ingredients of an isospin and momentum dependent transport model for
nuclear reactions induced by radioactive beams are outlined. Within the IBUU04
version of this model we study several experimental probes of the equation of
state of neutron-rich matter, especially the density dependence of the nuclear
symmetry energy. Comparing with the recent experimental data from NSCL/MSU on
isospin diffusion, we found a nuclear symmetry energy of $% E_{sym}(\rho
)\approx 31.6(\rho /\rho_{0})^{1.05}$ at subnormal densities. Predictions on
several observables sensitive to the density dependence of the symmetry energy
at supranormal densities accessible at GSI and the planned Rare Isotope
Accelerator (RIA) are also made.
