Walter, Jessika
[Verfasser:in]
;
Schuette
[Mitwirkende:r];
Peter Kramer
[Mitwirkende:r]
Averaging for Diffusive Fast-Slow Systems with Metastability in the Fast Variable ; Mittelung diffusiver Schnell-Langsamer Systeme mit Metastabilitaet in der Schnellen Variablen
Titel:
Averaging for Diffusive Fast-Slow Systems with Metastability in the Fast Variable ; Mittelung diffusiver Schnell-Langsamer Systeme mit Metastabilitaet in der Schnellen Variablen
Beteiligte:
Walter, Jessika
[Verfasser:in]
Erschienen:
Freie Universität Berlin: Refubium (FU Berlin), 2006
Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
Title Table of contents i 1\. Introduction to Conditional Averaging 1 1.1 The System under Consideration 2 1.2 The Averaging Principle 3 1.3 Breakdown of Averaging Principle 5 1.4 Conditional Averaging 7 1.5 Related Approaches 8 2\. Replacing Fast Dynamics by Coupled OU Processes 13 2.1 Guiding Remarks 13 2.2 Theory 16 2.3 Numerical Experiments 47 3\. Multiscale Asymptotics with Disparate Transition Scales 57 3.1 Guiding Remarks 57 3.2 Dominant Spectra and Metastability 59 3.3 Summary of Effective Dynamics 61 3.4 Multiscale Aymptotics and Averaging 70 3.5 Averaged Generator over ord(1) Time Scale 74 3.6 Multiscale Asymptotics with δ~ε 102 3.7 Multiscale Asymptotics with δ~ε2 107 4\. Concluding Remarks 123 Appendix A Zusammenfassung 127 B Averaging with Kurtz's Theorem 129 C Transition Times Considered in Full State Space (Sequel) 139 D Laplace's method 143 E Second Eigenvector of Lε: Illustrative Example 147 F Completion of Proof in Section 3.7.1 149 References 151 ; The thesis is based on conditional averaging of fast degrees of freedom (DOF). To this end, one considers gradient systems with different time scales: slow DOFs x that vary on a time scale of O(1) and fast DOFS y on a time scale of O(ε). Under certain conditions the fast variables can be eliminated from the original equation of motion by averaging according to the probability distribution corresponding to the exploration of the accessible fast state space. However, if the fast state space exhibit metatstable subsets, that is, subsets from which the fast motion will most probably exit only on some scale of order O(1) or even larger, the standard averagig scheme may fail to reproduce the effective dynamics of the original system. This problem can be solved by restricting the averaging procedure to the metastable subsets of the fast state space, respectively, and coupling the resulting averaged equations of motion in the slow variable x by means of a transition process; the associated rate matrix is then obtained by means of the expected exit times of ...