  We present a set of second-order, time-reversible algorithms for the
isothermal (NVT) molecular-dynamics (MD) simulation of systems with mixed
hard-core/continuous potentials. The methods are generated by combining
real-time Nose' thermostats with our previously developed Collision Verlet
algorithm [Mol. Phys. 98, 309 (1999)] for constant energy MD simulation of such
systems. In all we present 5 methods, one based on the Nose'-Hoover [Phys. Rev.
A 31, 1695 (1985)] equations of motion and four based on the Nose'-Poincare'
[J.Comp.Phys., 151 114 (1999)] real-time formulation of Nose' dynamics. The
methods are tested using a system of hard spheres with attractive tails and all
correctly reproduce a canonical distribution of instantaneous temperature. The
Nose'-Hoover based method and two of the Nose'-Poincare' methods are shown to
have good energy conservation in long simulations.
