### 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 |

### Fingerprint

### 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

**Multi-dimensional multicanonical algorithm, simulated tempering, replica-exchange method, and all that.** / Mitsutake, Ayori; Mori, Yoshiharu; Okamoto, Yuko.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Physics Procedia.*vol. 4, pp. 89-105, 23rd Annual Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics, Athens, GA, United States, 10/2/22. https://doi.org/10.1016/j.phpro.2010.08.012

}

TY - GEN

T1 - Multi-dimensional multicanonical algorithm, simulated tempering, replica-exchange method, and all that

AU - Mitsutake, Ayori

AU - Mori, Yoshiharu

AU - Okamoto, Yuko

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Generalized-ensemble algorithms

KW - Molecular dynamics

KW - Mont Carlo

KW - Multicanonical algorithm

KW - Parallel tempering

KW - Replica-exchange method

KW - Simulated tempering

UR - http://www.scopus.com/inward/record.url?scp=79551610888&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79551610888&partnerID=8YFLogxK

U2 - 10.1016/j.phpro.2010.08.012

DO - 10.1016/j.phpro.2010.08.012

M3 - Conference contribution

AN - SCOPUS:79551610888

VL - 4

SP - 89

EP - 105

BT - Physics Procedia

ER -