TY - CHAP A1 - Fischer, Alexander A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Cordes, Frank ED - Schlick, T. ED - Gan, H. T1 - Hierarchical Uncoupling-Coupling of Metastable Conformations T2 - Computational Methods for Macromolecules Y1 - 2002 UR - http://www.zib.de/PaperWeb/abstracts/ZR-01-03 IS - 24 SP - 235 EP - 259 PB - Springer ER - TY - JOUR A1 - Schütte, Christof A1 - Fischer, Alexander A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo JF - J. Comput. Phys. Y1 - 1999 UR - http://www.zib.de/PaperWeb/abstracts/SC-98-45 VL - 151 SP - 146 EP - 168 ER - TY - CHAP A1 - Schütte, Christof A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter ED - Fiedler, Bernold T1 - Transfer operator approach to conformational dynamics in biomolecular systems T2 - Ergodic theory, analysis, and efficient simulation of dynamical systems Y1 - 2001 SP - 191 EP - 223 PB - Berlin: Springer ER - TY - JOUR A1 - Deuflhard, Peter A1 - Huisinga, Wilhelm A1 - Fischer, Alexander A1 - Schütte, Christof T1 - Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains JF - Lin. Alg. Appl. Y1 - 2000 UR - http://publications.imp.fu-berlin.de/84/ U6 - https://doi.org/10.1016/S0024-3795(00)00095-1 VL - 315 IS - 1-3 SP - 39 EP - 59 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Dellnitz, M. A1 - Junge, Oliver A1 - Schütte, Christof ED - Deuflhard, Peter ED - Hermans, J. ED - Leimkuhler, Benedict ED - Marks, A. ED - Reich, Sebastian ED - Skeel, R. T1 - Computation of Essential Molecular Dynamics by Subdivision Techniques T2 - Computational Molecular Dynamics Y1 - 1999 UR - http://publications.mi.fu-berlin.de/135/ VL - 4 SP - 98 EP - 115 PB - Springer ER - TY - JOUR A1 - Schütte, Christof A1 - Fischer, Alexander A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter T1 - A Direct Approach to Conformational Dynamics based on Hybrid Monte Carlo JF - J. Comp. Phys Y1 - 1999 UR - http://publications.imp.fu-berlin.de/87/ U6 - https://doi.org/10.1006/jcph.1999.6231 VL - 151 IS - 1 SP - 146 EP - 168 ER - TY - CHAP A1 - Deuflhard, Peter A1 - Schütte, Christof ED - Hill, James ED - Moore, Ross T1 - Molecular Conformation Dynamics and Computational Drug Design T2 - Applied Mathematics Entering the 21st Century Y1 - 2004 UR - http://publications.imp.fu-berlin.de/125/ VL - 116 SP - 91 EP - 119 PB - SIAM ER - TY - CHAP A1 - Fischer, Alexander A1 - Schütte, Christof A1 - Deuflhard, Peter A1 - Cordes, Frank ED - Schlick, T. ED - Gan, H. T1 - Hierarchical Uncoupling-Coupling of Metastable Conformations T2 - Computational Methods for Macromolecules Y1 - 2002 UR - http://publications.imp.fu-berlin.de/128/ VL - 24 SP - 235 EP - 259 PB - Springer ER - TY - CHAP A1 - Schütte, Christof A1 - Huisinga, Wilhelm A1 - Deuflhard, Peter ED - Fiedler, B. T1 - Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems T2 - Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems Y1 - 2001 UR - http://publications.imp.fu-berlin.de/129/ SP - 191 EP - 223 PB - Springer ER - TY - GEN A1 - Deuflhard, Peter A1 - Dellnitz, Michael A1 - Junge, Oliver A1 - Schütte, Christof T1 - Computation of Essential Molecular Dynamics by Subdivision Techniques I: Basic Concept N2 - The paper presents the concept of a new type of algorithm for the numerical computation of what the authors call the {\em 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 to 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 just structurally connected via the underlying Frobenius-Perron theory. Numerical experiments with a first version of our suggested algorithm are included to illustrate certain distinguishing properties. A more advanced version of the algorithm will be presented in a second part of this paper. T3 - ZIB-Report - SC-96-45 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2553 ER -