6. Conclusion and outlook
To summarize, we provide a new algorithm for CPM simulations that forbids cell fragmentation (in addition to spontaneous nucleation) by testing the local connectivity of the candidate and target cells before every modification of a site value. It is shown that these two local connectivity tests are rigorously equivalent to testing the simple connectivity of the cells. This algorithm presents numerous advantages (and no drawbacks have been identified): • It improves the realism of the simulations of cellular systems (except perhaps for systems in pathological situations): no fragmentation or nucleation occurs, and cells stay simply connected. • For a same simulation temperature, it is faster than the standard algorithm used in CPM simulations: the time spent to test the local connectivity of the cells is largely offset by the time spared by not doing moves that induce fragmentation. • It restores detailed balance. As a consequence, the long-term stage and the statistics of configurations do not depend on the specific chosen acceptance rate, nor on the chosen path in the simulation temperature space: it depends only on the final temperature once the thermal equilibrium is reached. • It works for all simulation temperatures. Hence, when interested in the long-term stage of the simulations, we can (temporarily) increase the simulation temperature to converge more rapidly. • Its implementation is much easier than those of parallel algorithms.
