### Abstract

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E_{0} 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.

Original language | English |
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Title of host publication | Physics Procedia |

Pages | 89-105 |

Number of pages | 17 |

Volume | 4 |

DOIs | |

Publication status | Published - 2010 |

Event | 23rd Annual Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics - Athens, GA, United States Duration: 2010 Feb 22 → 2010 Feb 26 |

### Other

Other | 23rd Annual Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics |
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Country | United States |

City | Athens, GA |

Period | 10/2/22 → 10/2/26 |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Procedia*(Vol. 4, pp. 89-105) https://doi.org/10.1016/j.phpro.2010.08.012