Abstract
The paper presents basic concepts of a new type of algorithm for the numerical computation of what the authors call the essential dynamics of molecular systems. Mathematically speaking, such systems are described by Hamiltonian differential equations. In the bulk of applications, individual trajectories are of no specific interest. Rather, time averages of physical observables or relaxation times of conformational changes need to be actually computed. In the language of dynamical systems, such information is contained in the natural invariant measure (infinite relaxation time) or in almost invariant sets (“large” finite relaxation times). The paper suggests the direct computation of these objects via eigenmodes of the associated Frobenius-Perron operator by means of a multilevel subdivision algorithm. The advocated approach is different from both Monte-Carlo techniques on the one hand and long term trajectory simulation on the other hand: in our setup long term trajectories are replaced by short term sub-trajectories, Monte-Carlo techniques are connected via the underlying Frobenius-Perron structure. Numerical experiments with the suggested algorithm are included to illustrate certain distinguishing properties.
Dedicated to Prof. Dr. h.c. Roland Bulirsch on the occasion of his 65th birthday.
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Deuflhard, P., Dellnitz, M., Junge, O., Schütte, C. (1999). Computation of Essential Molecular Dynamics by Subdivision Techniques. In: Deuflhard, P., Hermans, J., Leimkuhler, B., Mark, A.E., Reich, S., Skeel, R.D. (eds) Computational Molecular Dynamics: Challenges, Methods, Ideas. Lecture Notes in Computational Science and Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58360-5_5
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DOI: https://doi.org/10.1007/978-3-642-58360-5_5
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