Metzner, Philipp
[Author]
;
Christof Schütte
[Contributor];
Eric Vanden-Eijnden
[Contributor]
Transition Path Theory for Markov Processes ; Application to Molecular Dynamics ; Übergangspfadtheorie für Markovprozesse ; Anwendung auf Moleküldynamik
You can manage bookmarks using lists, please log in to your user account for this.
Media type:
Doctoral Thesis;
Electronic Thesis;
E-Book
Title:
Transition Path Theory for Markov Processes ; Application to Molecular Dynamics ; Übergangspfadtheorie für Markovprozesse ; Anwendung auf Moleküldynamik
Contributor:
Metzner, Philipp
[Author]
Published:
Freie Universität Berlin: Refubium (FU Berlin), 2008
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
Title Table of contents i 1\. Introduction 1 2\. Theory: Time-continuous Markov Processes 9 3\. Transition Path Theory for Diffusion Processes 25 4\. Transition Path Theory for Markov Jump Processes 59 5\. Generator Estimation of Markov Jump Processes 91 6\. Detecting Reaction Pathways via Shortest Paths in Graphs 117 7\. Variance of the Committor Function 127 8\. Summary and Conclusion 143 Appendix 145 Zusammenfassung (deutsch) 174 References 177 ; In this thesis, we present the framework of transition path theory (TPT) for time continuous Markov processes with continuous and discrete state space. TPT provides statistical properties of the ensemble of reactive trajectories between some start and target sets and yields properties such as the committor function, the probability distribution of the reactive trajectories, their probability current and their rate of occurrence. We shown that knowing these objects allows one to arrive at a complete understanding of the mechanism of the reaction. The main objects of TPT for Markov diffusion processes are explicitly derived for the Langevin and Smoluchowski dynamics and illustrate them on a various number of low-dimensional examples. Despite the simplicity of these examples compared to those encountered in real applications, they already demonstrate the ability of TPT to handle complex dynamical scenarios. The main challenge in TPT for diffusion processes is the numerical computation of the committor function as a solution of a Dirichlet-Neumann boundary value problem involving the generator of the process. Beside the derivation of TPT for Markov jump processes, we focus on the development of efficient graph algorithms to determine reaction pathways in discrete state space. One approach via shortest-path algorithms turns out to give only a rough picture of possible reaction channels whereas the network approach allows a hierarchical decomposition of the set of reaction pathways such that the dominant channels can be identified. We successfully apply the latter approach ...