Lecture Notes in Computational Science and Engineering - Bioserver

232 Peter Blaudeck and Karl Heinz Hoffmann
to 36 Dual-Pentium-Boards and the send-receive functions of the common
MPI-software.
In Fig. 3 the new optimized schedules T(t) are displayed for different mass
densities. Note that our LDA scheme generally overestimates forces and potential
differences by a factor of about 1.5. Therefore, the mean values of both
the potential and the kinetic energy, and consequently also the temperature
differ from the real scale by this factor. The little time interval with constant
temperature at the end of the schedule has been added artificially to allow
the exact comparison of the final energies.
T (K)
8000
6000
4000
2000
0
mass−
density
(g/cm 3
)
3.52
3.0
2.7
0 1000 2000 3000 4000 5000
t
Fig. 3. Optimized annealing schedules (solid) for different mass densities, compared
with a previously used schedule (dotted)
The dotted line in Fig. 3 is an artificially constructed schedule used in
previous work. It was constructed based on the idea to find a sensible decreasing
function T(t) with a minimal descent at temperatures empirically known
as most important for structure formation processes. The full lines in Fig. 3
show, that this physical purpose has to be fulfilled still more rigorously by
the new optimized schedules. It seems quite clear that, compared with the old
schedules, the decrease in temperature is large at the very beginning of the
annealing process but much weaker in a temperature range where the most
important freezing of the structure is expected to take place. The schedules
depend on the mass density in a very plausible manner. The regions of weakest
descent consistently follow the temperatures which correspond sequently
to different “melting regions” for different binding energies per atom of these
structures. The lower the mass density, the less the average number of bonds
per atom, and, consequently, the lower the walls between the minima of the
potential energy.