We present the results of three-dimensional hydrodynamic calculations
of the evolution of low-mass molecular clouds, performed using the num
erical method of smoothed particle hydrodynamics. The clouds that we c
onsider are subject to heating by the interstellar radiation held and
by cosmic rays. They are able to cool through molecular line emission
(primarily CO and its isotopes) and by emission from the fine structur
e lines of C+ and O I. We also include gas-dust thermal coupling in ou
r models. A simplified chemical network is incorporated that models th
e conversion between C+ and CO, where the chemical balance is determin
ed by the local flux of dissociating radiation. Calculations are perfo
rmed for initially uniform density clouds, with masses in the range M=
100-400 M., sizes in the range R=1.7-3.4 pc, with the initial number d
ensity in all cases being n=100 cm(-3). We performed calculations for
clouds with different geometrical shapes: spherical, prolate, and obla
te. Additionally, we considered the effects of an anisotropic radiatio
n held on the cloud evolution. These are the main results: 1. Clouds t
hat are initially Jeans stable are able to collapse because of the cou
pling between the dynamical and thermal evolution. This collapse resul
ts in core-halo structure where we have a cold, dense, CO core surroun
ded by a warmer, tenuous, C+ envelope. 2. A pressure gradient is set u
p in the clouds by the attenuation of the UV radiation field. When a c
loud is anisotropically heated, this pressure gradient leads to the fo
rmation of a highly flattened cloud core when it collapses. 3. The com
bined thermal and dynamical evolution of the prolate and oblate clouds
leads to the formation of highly elongated or flattened structures. T
hese structures are able to fragment, typically with four to eight sub
condensations forming, which have masses in the range 3-7.5 M..