The purpose of this course is to give an in-depth overview to the theory and computational methods for the rare event studies. Some open issues will also be discussed. The students are required to have basic knowledge on stochastic ordinary differential equations. |
Lect01 Introduction: Formulation, examples and issues
Transition State Theory: RMP review 1990
Transition State Theory: Review 2005
Transition Path Theory: Review 2010
Part 1: Zero temperature regime
Lect02 Gradient system: LDT and transition path computation
Accelerated MD by OM functional
Lect03 Transition rate asymptotics: 1D and Multi-D
1D Rate formula by exit problem
Multi-D Rate formula by exit problem
Lect04 Saddle points finding: Dimer, GAD etc.
Lect05 Non-gradient sytems: CKS, Large volume limit and LDT
Application in phenotype switching
Two-scale LDT by path integral
Lect06 Energy landscape and gMAM
Lect07 Non-gradient systems: Difficulties and unsolved issues
Maier-Stein PRL: non-Arrhenius law
Lect08 Onsager-Machlup and Freidlin-Wentzell dilemma
Lect09 Spectral theory approach and applications
Part 2: Finite temperate case
Lect10 Potential theory for Markov processes: I
Lect11 Potential theory for Markov processes: II
Syski's book: Passage times for Markov chains
Lect12 Transtion path theory: Diffusion and jump models
Lect13 Finite temperature string method
Lect14 Markov state modeling: Formulation and computation
Lect15 Markov state modeling: Analysis and applications
Part 3: Sampling approach
Lect16 Accelerated MD, TAMD, AFED etc.
Lect17 Umbrella sampling, meta-dynamics, replica exchange etc