### Abstract

We study the coupling between shape changes and rotations of molecules in a random environment. As a prototype of molecules or biopolymers that can undergo non-trivial conformational transitions we consider a planar four-atomic molecule, with underdamped dynamics of Langevin-type. In this simplified setting, we can extend the available gauge theory of semi-flexible molecules to the stochastic setting which allows us to analyse and explain geometric phase effects that arise from the internal motion of the molecule. Due to the stochastic nature of the Langevin system, the internal dynamics contains temperature-dependent coriolis forces that arise from the fluctuations of the angular momentum around its mean value zero. All theoretical investigations are supplemented by numerical simulations, in which we specifically investigate the dependence of the orientational shift on the parameters of the Langevin equation, i.e., friction coefficient, atomic masses, temperature and the velocity of deformation of the system. The numerical results confirm our theoretical findings. We further discuss various extension of the analysis, e.g., to the overdamped limit or optimal control.

Original language | English |
---|---|

Pages (from-to) | 3534-3545 |

Number of pages | 12 |

Journal | Molecular Physics |

Volume | 111 |

Issue number | 22-23 |

DOIs | |

Publication status | Published - 2013 Dec 1 |

### Fingerprint

### Keywords

- Fixman potential
- Geometric phase
- Langevin equation
- Nonlinear dynamics

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Condensed Matter Physics
- Biophysics
- Molecular Biology

### Cite this

*Molecular Physics*,

*111*(22-23), 3534-3545. https://doi.org/10.1080/00268976.2013.831956

**The falling cat problem and shape effects in small molecules in a random environment : A case study.** / Hartmann, Carsten; Yanao, Tomohiro.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 111, no. 22-23, pp. 3534-3545. https://doi.org/10.1080/00268976.2013.831956

}

TY - JOUR

T1 - The falling cat problem and shape effects in small molecules in a random environment

T2 - A case study

AU - Hartmann, Carsten

AU - Yanao, Tomohiro

PY - 2013/12/1

Y1 - 2013/12/1

N2 - We study the coupling between shape changes and rotations of molecules in a random environment. As a prototype of molecules or biopolymers that can undergo non-trivial conformational transitions we consider a planar four-atomic molecule, with underdamped dynamics of Langevin-type. In this simplified setting, we can extend the available gauge theory of semi-flexible molecules to the stochastic setting which allows us to analyse and explain geometric phase effects that arise from the internal motion of the molecule. Due to the stochastic nature of the Langevin system, the internal dynamics contains temperature-dependent coriolis forces that arise from the fluctuations of the angular momentum around its mean value zero. All theoretical investigations are supplemented by numerical simulations, in which we specifically investigate the dependence of the orientational shift on the parameters of the Langevin equation, i.e., friction coefficient, atomic masses, temperature and the velocity of deformation of the system. The numerical results confirm our theoretical findings. We further discuss various extension of the analysis, e.g., to the overdamped limit or optimal control.

AB - We study the coupling between shape changes and rotations of molecules in a random environment. As a prototype of molecules or biopolymers that can undergo non-trivial conformational transitions we consider a planar four-atomic molecule, with underdamped dynamics of Langevin-type. In this simplified setting, we can extend the available gauge theory of semi-flexible molecules to the stochastic setting which allows us to analyse and explain geometric phase effects that arise from the internal motion of the molecule. Due to the stochastic nature of the Langevin system, the internal dynamics contains temperature-dependent coriolis forces that arise from the fluctuations of the angular momentum around its mean value zero. All theoretical investigations are supplemented by numerical simulations, in which we specifically investigate the dependence of the orientational shift on the parameters of the Langevin equation, i.e., friction coefficient, atomic masses, temperature and the velocity of deformation of the system. The numerical results confirm our theoretical findings. We further discuss various extension of the analysis, e.g., to the overdamped limit or optimal control.

KW - Fixman potential

KW - Geometric phase

KW - Langevin equation

KW - Nonlinear dynamics

UR - http://www.scopus.com/inward/record.url?scp=84889568755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889568755&partnerID=8YFLogxK

U2 - 10.1080/00268976.2013.831956

DO - 10.1080/00268976.2013.831956

M3 - Article

AN - SCOPUS:84889568755

VL - 111

SP - 3534

EP - 3545

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 22-23

ER -