@article{545c8205df424aefbe8be76df76e5fd9,

title = "Multi-dimensional multicanonical algorithm, simulated tempering, replica-exchange method, and all that",

abstract = "We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E0 by adding any physical quantity V of interest as a new energy term with a coupling constant λ. We then perform a multi-dimensional multicanonical simulation where a random walk in E 0 and V space is realized. We can alternately perform a multi-dimensional simulated-tempering simulation where a random walk in temperature T and parameter λ is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations. Two examples of the above methods are presented for biomoleculr systems where the parameter λ corresponds to the solvation parameter and the pressure. In the former, a random walk in the conformational energy and solvation free energy is performed, and in the latter, a random walk in the potential energy and volume is realized.",

keywords = "Generalized-ensemble algorithms, Molecular dynamics, Mont Carlo, Multicanonical algorithm, Parallel tempering, Replica-exchange method, Simulated tempering",

author = "Ayori Mitsutake and Yoshiharu Mori and Yuko Okamoto",

note = "Funding Information: The multi-dimensional generalized-ensemble algorithms that were presented in the present article will be very useful for Monte Carlo and molecular dynamics simulations of complex systems such as spin glass, molecular, polymer, and biopolymer systems. Acknowledgements: Some of the results were obtained by the computations on the super computers at the Institute for Molecular Science, Okazaki, Japan. This work was supported, in part, by Grants-in-Aid for Scientific Research in Priority Areas (“Water and Biomolecules” and “Molecular Theory for Real Systems”), for Scientific Research on Innovative Areas (“Fluctuations and Biological Functions” ), and for the Next Generation Super Computing Project, Nanoscience Program from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.",

year = "2010",

doi = "10.1016/j.phpro.2010.08.012",

language = "English",

volume = "4",

pages = "89--105",

journal = "Physics Procedia",

issn = "1875-3884",

publisher = "Elsevier BV",

}