Repository: Freie Universit├Ąt Berlin, Math Department

The falling cat problem and shape effects in small molecules in a random environment: a case study

Hartmann, C. and Yanao, Tomohiro (2013) The falling cat problem and shape effects in small molecules in a random environment: a case study. Molecular Physics, 111 (22-23). pp. 3534-3545. ISSN 0026-8976

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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 nontrivial confor- mational 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 analyze 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 equa- tion, 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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
Other Institutes > Matheon > A - Life Sciences
Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:1298
Deposited By: Carsten Hartmann
Deposited On:01 Jul 2013 13:05
Last Modified:03 Mar 2017 14:41

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