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Numerical schemes are presented for dynamical systems with multiple time-scales. Two classes of methods are discussed, depending on the time interval on which the evolution of the slow variables inâ€¦ (More)

- Frank NoÃ©, Christof SchÃ¼tte, Eric Vanden-Eijnden, Lothar Reich, Thomas R. Weikl
- Proceedings of the National Academy of Sciencesâ€¦
- 2009

Characterizing the equilibrium ensemble of folding pathways, including their relative probability, is one of the major challenges in protein folding theory today. Although this information is inâ€¦ (More)

A new approach is proposed for stochastic parameterization of subgrid scale processes in models of atmospheric or oceanic circulation. The new approach relies on two key ingredients. First, theâ€¦ (More)

- Bjorn Engquist, Xiantao Li, W. Ren, Eric Vanden-Eijnden
- 2007

This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods, including the fundamental design principles behind the HMM philosophy and the main obstacles that have to beâ€¦ (More)

- Luca Maragliano, Alexander U Fischer, Eric Vanden-Eijnden, Giovanni Ciccotti
- The Journal of chemical physics
- 2006

A computational technique is proposed which combines the string method with a sampling technique to determine minimum free energy paths. The technique only requires to compute the mean force andâ€¦ (More)

- Weinan E, Tiejun Li, Eric Vanden-Eijnden
- Proceedings of the National Academy of Sciencesâ€¦
- 2008

Given a large and complex network, we would like to find the best partition of this network into a small number of clusters. This question has been addressed in many different ways. Here we propose aâ€¦ (More)

This study applies a systematic strategy for stochastic modeling of atmospheric low-frequency variability to a realistic barotropic model climate. This barotropic model climate has reasonableâ€¦ (More)

Metropolized integrators for ergodic stochastic differential equations (SDEs) are proposed that (1) are ergodic with respect to the (known) equilibrium distribution of the SDEs and (2) approximateâ€¦ (More)

- Weinan E, Weiqing Ren, Eric Vanden-Eijnden
- The Journal of chemical physics
- 2007

We present a simplified and improved version of the string method, originally proposed by E et al. [Phys. Rev. B 66, 052301 (2002)] for identifying the minimum energy paths in barrier-crossingâ€¦ (More)

- Philipp Metzner, Christof SchÃ¼tte, Eric Vanden-Eijnden
- Multiscale Modeling & Simulation
- 2008

The framework of transition path theory (TPT) is developed in the context of continuous-time Markov chains on discrete state-spaces. Under assumption of ergodicity, TPT singles out any two subsets inâ€¦ (More)