A conjecture about molecular dynamics. (English) Zbl 1391.82050
Munthe-Kaas, Hans (ed.) et al., Mathematics and computation, a contemporary view. The Abel symposium 2006. Proceedings of the third Abel symposium, Alesund, Norway, May 25–27, 2006. Berlin: Springer (ISBN 978-3-540-68848-8/hbk). Abel Symposia 3, 95-108 (2008).
Summary: An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is believed that statistical information from these simulations is accurate, but no one has offered a rigourous proof of this. In order to give mathematicians a clear goal in understanding this problem, we state a precise mathematical conjecture about molecular dynamics simulation of a particular system. We believe that if the conjecture is proved, we will then understand why molecular dynamics works.
For the entire collection see [Zbl 1148.00004].
For the entire collection see [Zbl 1148.00004].
MSC:
| 82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
| 37M05 | Simulation of dynamical systems |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 82D99 | Applications of statistical mechanics to specific types of physical systems |
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