Open Access
Issue |
ESAIM: PS
Volume 27, 2023
|
|
---|---|---|
Page(s) | 723 - 748 | |
DOI | https://doi.org/10.1051/ps/2023012 | |
Published online | 31 July 2023 |
- A. Barducci, G. Bussi and M. Parrinello, Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys. Rev. Lett. 100 (2008) 020603. [CrossRef] [PubMed] [Google Scholar]
- M. Benaïm and C.-E. Bréhier, Convergence analysis of adaptive biasing potential methods for diffusion processes. Commun. Math. Sci. 17 (2019) 81–130. [CrossRef] [MathSciNet] [Google Scholar]
- M. Benaïm, C.-E. Bréhier and P. Monmarché, Analysis of an Adaptive Biasing Force method based on self-interacting dynamics. Electron. J. Probab. (2020), in press. [Google Scholar]
- M. Ceriotti, G. Bussi and M. Parrinello, Colored-noise thermostats á la carte. J. Chem. Theory Comput. 6 (2010) 1170–1180. [CrossRef] [Google Scholar]
- M.V. Day, On the exponential exit law in the small parameter exit problem. Stochastics 8 (1983) 297–323. [CrossRef] [MathSciNet] [Google Scholar]
- A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Vol. 38 of Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin (2010). Corrected reprint of the second (1998) edition. [CrossRef] [Google Scholar]
- M.H. Duong and J. Tugaut, Coupled McKean–Vlasov diffusions: wellposedness, propagation of chaos and invariant measures. Stochastics 92 (2020) 900–943. [CrossRef] [MathSciNet] [Google Scholar]
- V. Ehrlacher, T. Lelièvre and P. Monmarché. Adaptive force biasing algorithms: new convergence results and tensor approximations of the bias. Working paper or preprint, July 2020. [Google Scholar]
- G. Fort, B. Jourdain, T. Lelièvre and G. Stoltz, Convergence and efficiency of adaptive importance sampling techniques with partial biasing. J. Stat. Phys. 171 (2018) 220–268. [CrossRef] [MathSciNet] [Google Scholar]
- M.I. Freidlin, Some remarks on the Smoluchowski-Kramers approximation. J. Stat. Phys. 117 (2004) 617–634. [CrossRef] [Google Scholar]
- M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems, Vol. 260 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edn. Springer-Verlag, New York (1998). Translated from the 1979 Russian original by Joseph Szücs. [CrossRef] [Google Scholar]
- R.A. Holley, S. Kusuoka and D.W. Stroock, Asymptotics of the spectral gap with applications to the theory of simulated annealing. J. Funct. Anal. 83 (1989) 333–347. [CrossRef] [MathSciNet] [Google Scholar]
- B. Jourdain, T. Lelièvre and P.-A. Zitt, Convergence of metadynamics: discussion of the adiabatic hypothesis. arXiv preprint arXiv:1904.08667, 2019. [Google Scholar]
- A. Laio and M. Parrinello, Escaping free-energy minima. Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 12562–12566. [CrossRef] [PubMed] [Google Scholar]
- B. Leimkuhler and M. Sachs, Efficient Numerical Algorithms for the Generalized Langevin Equation. arXiv e-prints, page arXiv:2012.04245, December 2020. [Google Scholar]
- T. Lelièvre, Two mathematical tools to analyze metastable stochastic processes, in Numerical Mathematics and Advanced Applications 2011. Springer, Heidelberg (2013) 791–810. [CrossRef] [Google Scholar]
- T. Lelièvre, M. Rousset and G. Stoltz, Long-time convergence of an adaptive biasing force method. Nonlinearity 21 (2008) 1155–1181. [CrossRef] [MathSciNet] [Google Scholar]
- T. Lelièvre, M. Rousset and G. Stoltz, Free Energy Computations: A Mathematical Perspective. Imperial College Press (2010). [CrossRef] [Google Scholar]
- T. Lelièvre and G. Stoltz, Partial differential equations and stochastic methods in molecular dynamics. Acta Numerica 25 (2016) 681–880. [CrossRef] [MathSciNet] [Google Scholar]
- P. Monmarché, Almost sure contraction for diffusions on ℝd. Application to generalised Langevin diffusions. arXiv e-prints, page arXiv:2009.10828, September 2020. [Google Scholar]
- M. Ottobre and G.A. Pavliotis, Asymptotic analysis for the generalized Langevin equation. Nonlinearity 24 (2011) 1629–1653. [CrossRef] [MathSciNet] [Google Scholar]
- L. Stella, C.D. Lorenz and L. Kantorovich, Generalized langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems. Phys. Rev. B 89 (2014) 134303. [CrossRef] [Google Scholar]
- D.W. Stroock and S.R. Srinivasa Varadhan, Multidimensional Diffusion Processes, Vol. 233 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin-New York (1979). [Google Scholar]
- J. Tugaut, Exit problem of McKean-Vlasov diffusions in convex landscapes. Electron. J. Probab. 17 (2012) 26. [CrossRef] [Google Scholar]
- J. Tugaut, A simple proof of a Kramers’ type law for self-stabilizing diffusions. Electron. Commun. Probab. 21 (2016) 7. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.